Model: gemini-3-pro-preview

# Spatial Exploration Task

You are a spatial reasoner in a 2D, text-only N×M grid. Every object including you is a point at integer (x, y) coordinates.

Goal: **Minimize total COST** while building a complete and accurate map of the environment.

Multi-room rules (may exist multiple rooms):
- Your vision is confined to your current room.
- Doors block vision between rooms.
- Exception: When located in a doorway, door is open and invisible, you can see into both connected rooms.
- Rooms connect via doors on vertical (front/back) or horizontal (left/right) walls.


Relationship instructions:
Relationship: bearing in degrees; distance is Euclidean. Use binned labels.
Bearing is a degree in [-180, 180]; 0° is front. +: clockwise, -: counterclockwise.
Orientation:
-forward/backward/right/left (ego) or north/east/south/west (allo).
-When agent faces north: forward = north, right = east, etc.
-Gate's orientation: report wall position (e.g., 'on left wall').
Binned relationship reporting:
EgoFront (egocentric, object-to-agent); Cardinal (object-to-object).
Egocentric angle bins (0° is front): [-45°,-22.5°)→front-left, [-22.5°,0°)→front-slight-left, 0°→front, (0°,22.5°]→front-slight-right, (22.5°,45°]→front-right, otherwise→beyond-fov.
Cardinal angle bins (45° each): (-22.5°,22.5°]→north, (22.5°,67.5°]→north east, (67.5°,112.5°]→east, (112.5°,157.5°]→south east, (157.5°,202.5°]→south, (202.5°,247.5°]→south west, (247.5°,292.5°]→west, (292.5°,337.5°]→north west,
Distance bins: =0→same distance, (0,2]→near, (2,4]→mid distance, (4,8]→slightly far, (8,16]→far, (16,32]→very far, 32→extremely far.
Proximity: relations between close objects (≤2.0m). Use cardinal directions and standard distance bins.

Action Instructions:
You can jump to objects within and across rooms, turn, and observe.
When you are at a door, you can see objects from both connected rooms (within FOV).

Available Actions:
Movement (<M>):
- JumpTo(OBJ): Jump to the same position as the object or door. Your orientation does NOT change. The object you jump to MUST be in your field of view and previously observed. Use object or door names only. NO numbers or directions or others. Invalid: JumpTo(left), JumpTo(1).
- Rotate(DEG): Rotate relative to your current orientation. Positive = clockwise, negative = counterclockwise. Valid: -270, -180, -90, 0, 90, 180, 270. You must rotate by these specified degrees; otherwise your action will be invalid.
Final (<F>):
- Observe(): Report objects (including doors) and their spatial relationships from your current position in your FOV. Also reports relations between mutually close objects in your FOV, using your current facing direction as north (a relative reference frame, not true north).Use exactly one Observe() per step and make it the last action. Never call Term() after Observe().
- Query(obj): Return object's coordinates with agent's initial position as origin, north as y+ axis. You can only query objects that you have previously observed. High cost, only use when necessary to eliminate ambiguities.
- Term(): Terminate the exploration phase. Term() must be alone with no movement actions. You MUST ONLY use it in the last turn and no other turns. Otherwise your action sequence will be invalid.

Action Grammar (HARD CONSTRAINT):
Actions: [ <M>* <F> ]
<M> = "JumpTo(OBJ)" | "Rotate(DEG)"
<F> = "Observe()" | "Query(OBJ)" | "Term()"
Constraints:
- Zero, one or more <M>. No JumpTo at first step.
- Exactly one <F>, and it must be the final action.
- No more than one Observe().
- Term() may appear only alone.
- Any violation is invalid.

Examples:
Valid: Actions: [JumpTo(red door), Rotate(90), JumpTo(table), Observe()]
Valid: Actions: [Observe()] | Query(table)
Invalid (no final action): Actions: [JumpTo(table)]
Invalid (more than one final action): Actions: [Observe(), Rotate(90), Observe()]
Invalid (termination with other actions): Actions: [JumpTo(table), Term()]


Rules:
- Observe action only reports from your current position and facing direction. If you jump multiple times, the final Observe() action gives the view only from your last position.
- Actions execute in order. Field of view: 90°.

Observe and Query action have costs:
- Observe(): 1
- Query(obj): 2


Rules:
- Achieve complete coverage with the fewest steps;
- Prefer actions that reveal more unknowns; avoid redundancy
- FOV is 90°, you can NOT see objects outside your FOV.
- Track your current and initial pose


Room Layout and initial state:
Imagine 3 rooms connected by doors: room 1, room 2, room 3. You current (initial) position is in room 1 and you face north. Unless otherwise specified, treat your initial position as the origin (0, 0), and north is +y.
Objects: 1: shoes, 2: shoppingcart, 3: laptop, 4: rubberduck, 5: bike, 6: airplane, 7: pan, 8: alarmclock, 9: red chair, 10: backpack, 11: desklamp, 12: books
Doors: yellow door, blue door


You have a maximum of 20 exploration steps.



Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

# Spatial Exploration Task

You are a spatial reasoner in a 2D, text-only N×M grid. Every object including you is a point at integer (x, y) coordinates.

Goal: **Minimize total COST** while building a complete and accurate map of the environment.

Multi-room rules (may exist multiple rooms):
- Your ...

The agent is at the starting position (0,0) in Room 1, facing North. The goal is to map the environment with minimum cost. To do this, the agent must first discover objects or doors to move to. Since the agent cannot jump to an object it hasn't seen yet, the only valid first action is to observe the current field of view. This will reveal any objects or doors in the northern quadrant (front).

The agent is at the starting position (0,0) in Room 1, facing North. The goal is to map the environment with minimum cost. To do this, the agent must first discover objects or doors to move to. Since the agent cannot jump to an object it hasn't seen yet, the only valid first action is to observe the...

THINK:
The agent is at [0,0] facing North. The observation revealed no objects in the field of view. Therefore, the cognitive map only contains the agent at its current position.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"}
}
```

THINK:
The agent is at [0,0] facing North. The observation revealed no objects in the field of view. Therefore, the cognitive map only contains the agent at its current position.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"}
}
```...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

THINK:
The agent observed no objects in the current field of view (North). Therefore, the list of objects in the local cognitive map is empty.

FINAL ANSWER:
{
"origin": "agent",
"objects": {}
}

THINK:
The agent observed no objects in the current field of view (North). Therefore, the list of objects in the local cognitive map is empty.

FINAL ANSWER:
{
"origin": "agent",
"objects": {}
}...

{
  "origin": "agent",
  "objects": {}
}

{
  "origin": "agent",
  "objects": {}
}

THINK: The agent is at `*` facing North (Up) and has just performed `Observe()`. This action reveals the cone of vision 45 degrees to the left and right of North.
Based on the grid map:
- Points `D` (directly North), `B` (North-North-East), and `C` (North-East, exactly 45 degrees) fall within the observed field of view. The instruction for bins specifies `(22.5°,45°]` is "front-right", which is within the FOV. Thus, D, B, and C are in the explored region.
- Point `E` is located significantly to the East (Right) of the agent (approx 78 degrees relative to North). This is outside the 45-degree FOV limit. Thus, E is unexplored.
- Point `F` is to the South-East (behind and right). This is outside the FOV. Thus, F is unexplored.
- Point `A` is to the South (behind). This is outside the FOV. Thus, A is unexplored.

Therefore, the points in unexplored/unobserved regions are A, E, and F.

FINAL ANSWER:
```json
{
"unexplored": ["A", "E", "F"]
}
```

THINK: The agent is at `*` facing North (Up) and has just performed `Observe()`. This action reveals the cone of vision 45 degrees to the left and right of North.
Based on the grid map:
- Points `D` (directly North), `B` (North-North-East), and `C` (North-East, exactly 45 degrees) fall within the ob...

################
#########......#
#########......#
##DBC...#......#
##.....E#......#
##*.....#......#
##.....F+......#
##......########
##.A....########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You observe: No objects in field of view..
You have a maximum of 19 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You observe: No objects in field of view..
You have a maximum of 19 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at (0,0) in Room 1 facing North and saw nothing in the previous observation. To discover objects and doors, the agent must look in different directions. Rotating 90 degrees clockwise to face East is a logical next step to scan the room.

The agent is at (0,0) in Room 1 facing North and saw nothing in the previous observation. To discover objects and doors, the agent must look in different directions. Rotating 90 degrees clockwise to face East is a logical next step to scan the room....

THINK: [The agent is at (0,0) facing East. Based on the observations and relative constraints:
- "alarmclock" is at (2,1) (front-left, mid dist) facing West.
- "rubberduck" is at (2,-1) (front-right, mid dist) facing North.
- "shoes" is at (4,-1) (front-slight-right, slightly far) facing West.
- "yellow door" is at (5,-1) (front-slight-right, slightly far, on front/East wall).
- "blue door" is at (4,-3) (front-right, slightly far, on right/South wall).
The relative positions confirm: Shoes (East of Rubberduck, West of Yellow Door), Rubberduck (South of Alarmclock). The doors are likely on the boundaries of Room 1.]
FINAL ANSWER: {"agent": {"position": [0, 0], "facing": "east"}, "alarmclock": {"position": [2, 1], "facing": "west"}, "rubberduck": {"position": [2, -1], "facing": "north"}, "shoes": {"position": [4, -1], "facing": "west"}, "yellow door": {"position": [5, -1]}, "blue door": {"position": [4, -3]}}

THINK: [The agent is at (0,0) facing East. Based on the observations and relative constraints:
- "alarmclock" is at (2,1) (front-left, mid dist) facing West.
- "rubberduck" is at (2,-1) (front-right, mid dist) facing North.
- "shoes" is at (4,-1) (front-slight-right, slightly far) facing West.
- "ye...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      5,
      -1
    ]
  },
  "blue door": {
    "position": [
      4,
      -3
    ]
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  }
}

THINK: [The agent is facing Global East (local +y). The observations reveal a room layout with objects and two doors. Using the proximity rules and bins:
1. **alarmclock**: Front-left, mid-distance. Placed at (-2, 3).
2. **rubberduck**: Front-right, mid-distance. "East" of alarmclock implies higher X. Placed at (2, 3). This satisfies "mid distance" from agent and distance 4 from alarmclock.
3. **shoes**: Front-slight-right, slightly far. "North" of rubberduck implies higher Y. Placed at (2, 5). Distance 2 from rubberduck is "near".
4. **yellow door**: Front-slight-right, slightly far. "Shoes is south, near to yellow door" implies yellow door is North of shoes. Placed at (2, 7). On "front wall" means facing -y (towards agent).
5. **blue door**: Front-right, slightly far. On "right wall" means facing -x. Placed at (5, 6) to fit "slightly far" and angle bins.]

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"shoes": {"position": [2, 5], "facing": "-y"},
"rubberduck": {"position": [2, 3], "facing": "-x"},
"alarmclock": {"position": [-2, 3], "facing": "-y"},
"yellow door": {"position": [2, 7], "facing": "-y"},
"blue door": {"position": [5, 6], "facing": "-x"}
}
}
```

THINK: [The agent is facing Global East (local +y). The observations reveal a room layout with objects and two doors. Using the proximity rules and bins:
1. **alarmclock**: Front-left, mid-distance. Placed at (-2, 3).
2. **rubberduck**: Front-right, mid-distance. "East" of alarmclock implies highe...

{
  "origin": "agent",
  "objects": {
    "shoes": {
      "position": [
        2,
        5
      ],
      "facing": "-y"
    },
    "rubberduck": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "alarmclock": {
      "position": [
        -2,
        3
      ],
      "facing": "-y"
    },
    "yellow door": {
      "position": [
        2,
        7
      ],
      "facing": "-y"
    },
    "blue door": {
      "position": [
        5,
        6
      ],
      "facing": "-x"
    }
  }
}

{
  "shoes": {
    "position": [
      1,
      4
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "alarmclock": {
    "position": [
      -1,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      4,
      4
    ],
    "facing": "north"
  },
  "rubberduck": {
    "position": [
      1,
      2
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "shoes": {
      "position": [
        2,
        5
      ],
      "facing": "-y"
    },
    "rubberduck": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "alarmclock": {
      "position": [
        -2,
        3
      ],
      "facing": "-y"
    },
    "yellow door": {
      "position": [
        2,
        7
      ],
      "facing": "-y"
    },
    "blue door": {
      "position": [
        5,
        6
      ],
      "facing": "-x"
    }
  }
}

{
  "shoes": {
    "position": [
      1,
      4
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "alarmclock": {
    "position": [
      -1,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      4,
      4
    ],
    "facing": "north"
  },
  "rubberduck": {
    "position": [
      1,
      2
    ],
    "facing": "north"
  }
}

THINK: The agent has observed twice: once facing North and once facing East.
1. **Observe (North)**: The field of view (FOV) covered the cone from North-West to North-East (45° to 135° in standard Cartesian terms). No objects were seen.
2. **Observe (East)**: The agent rotated 90° clockwise. The FOV now covers the cone from North-East to South-East (-45° to 45° relative to East, or -45° to +45° standard). Objects A, C, D fall within this cone.
- **C** (approx. North-East) is in the overlap or just inside the East view.
- **D** (approx. East) is directly in front.
- **A** (approx. South-East, dx=1, dy=-1 relative to agent) is at +45° (Clockwise) relative to the agent's facing, which falls into the "front-right" bin.
3. **Unexplored Points**:
- **F** is directly South of the agent. This is 90° clockwise from East, which is outside the 45° half-angle of the FOV. It was also behind the agent during the North observation.
- **E** is South-South-East (dx=1, dy=-2). The angle is approx 63° clockwise from East. This is outside the 45° limit. It was not visible in the North view either.
- **B** is directly South (further down). Outside both FOVs.

Therefore, F, E, and B are in unobserved regions.

FINAL ANSWER:
```json
{
"unexplored": ["B", "E", "F"]
}
```

THINK: The agent has observed twice: once facing North and once facing East.
1. **Observe (North)**: The field of view (FOV) covered the cone from North-West to North-East (45° to 135° in standard Cartesian terms). No objects were seen.
2. **Observe (East)**: The agent rotated 90° clockwise. The ...

################
#########......#
#########......#
##....C.#......#
##.....D#......#
##*.....#......#
##FA....+......#
##.E....########
##B.....########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You rotated clockwise 90°. You observe:
• shoes: front-slight-right, slightly far, facing backward
• rubberduck: front-right, mid distance, facing left
• alarmclock: front-left, mid distance, facing backward
• yellow door: front-slight-right, slightly far, on front wall
• blue door: front-right, slightly far, on right wall
Assume your current facing direction is called "north":
• shoes is north, near to rubberduck
• shoes is south, near to yellow door
• rubberduck is east, near to alarmclock.
You have a maximum of 18 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• shoes: front-slight-right, slightly far, facing backward
• rubberduck: front-right, mid distance, facing left
• alarmclock: front-left, mid distance, facing backward
• yellow door: front-slight-right, slightly far, on front wall
• blue door: front-right, sl...

The agent is currently at (0,0) facing East. The previous observation revealed a "yellow door" on the front wall (East) and a "blue door" on the right wall (South). To proceed with mapping, the agent should explore one of the connected rooms. The "yellow door" is in the direction the agent is currently facing. Jumping to the "yellow door" will place the agent in the doorway. Since the agent is facing East and the door is on the East wall, observing from this position will allow the agent to see into the new room (Room 2) while maintaining the current orientation.

The agent is currently at (0,0) facing East. The previous observation revealed a "yellow door" on the front wall (East) and a "blue door" on the right wall (South). To proceed with mapping, the agent should explore one of the connected rooms. The "yellow door" is in the direction the agent is curren...

THINK: The agent has moved to the "yellow door" located at the boundary between Room 1 and Room 2. From this vantage point (facing East), the agent observes Room 2. Based on the previous and current observations, I can construct a coordinate map.
Room 1 (explored from (0,0)):
- Agent started at (0,0).
- "alarmclock" is at approx (3, 2) (front-left, mid dist).
- "rubberduck" is at approx (3, -2) (front-right, mid dist).
- "shoes" is near "rubberduck" but further east ("north" relative to facing East), approx (5, -2).
- "yellow door" is east of "shoes" ("south" relative to facing East), approx (6, -2).
- "blue door" is on the right wall (South wall), approx (4, -4).

Room 2 (observed from "yellow door" at (6, -2), facing East):
- "books" is directly front (East), mid distance (~3 units), approx (9, -2).
- "laptop" is north of books ("west" relative to facing East), and west of backpack. Position approx (9, 0).
- "backpack" is east of laptop ("south" relative to facing East), approx (11, 0).
- "airplane" is north of backpack ("west" relative to facing East), approx (11, 2).

Object orientations were reported relative to agent's facing (East).
- shoes: facing backward (West).
- rubberduck: facing left (North).
- alarmclock: facing backward (West).
- laptop: facing forward (East).
- airplane: facing right (South).
- backpack: facing left (North).

FINAL ANSWER:
```json
{
"agent": {"position": [6, -2], "facing": "east"},
"alarmclock": {"position": [3, 2], "facing": "west"},
"rubberduck": {"position": [3, -2], "facing": "north"},
"shoes": {"position": [5, -2], "facing": "west"},
"yellow door": {"position": [6, -2]},
"blue door": {"position": [4, -4]},
"laptop": {"position": [9, 0], "facing": "east"},
"airplane": {"position": [11, 2], "facing": "south"},
"backpack": {"position": [11, 0], "facing": "north"},
"books": {"position": [9, -2]}
}
```

THINK: The agent has moved to the "yellow door" located at the boundary between Room 1 and Room 2. From this vantage point (facing East), the agent observes Room 2. Based on the previous and current observations, I can construct a coordinate map.
Room 1 (explored from (0,0)):
- Agent started at (0,0...

{
  "agent": {
    "position": [
      6,
      -2
    ],
    "facing": "east"
  },
  "alarmclock": {
    "position": [
      3,
      2
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      3,
      -2
    ],
    "facing": "north"
  },
  "shoes": {
    "position": [
      5,
      -2
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      6,
      -2
    ]
  },
  "blue door": {
    "position": [
      4,
      -4
    ]
  },
  "laptop": {
    "position": [
      9,
      0
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      11,
      2
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      11,
      0
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      9,
      -2
    ]
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  }
}

THINK: [The agent is at the yellow door facing East. The observation reveals four objects in what appears to be Room 2. Based on the relative descriptions (front/front-left) and distance bins (mid/slightly far), I can estimate local coordinates. "Front" corresponds to local +y, "Left" to local -x. Using the provided proximity relations (e.g., "laptop is south of backpack" relative to the facing direction) helps refine the positions. Distances are checked against bins: Books (dist ~3, mid), Laptop (dist ~4.5, slightly far), Airplane (dist ~5.8, slightly far), Backpack (dist ~6.1, slightly far). Facings are mapped to local axes: "facing forward" -> +y, "facing right" -> +x, "facing left" -> -x.]
FINAL ANSWER: [
{
"origin": "agent",
"objects": {
"laptop": {"position": [-2, 4], "facing": "+y"},
"airplane": {"position": [-3, 5], "facing": "+x"},
"backpack": {"position": [-1, 6], "facing": "-x"},
"books": {"position": [0, 3]}
}
}
]

THINK: [The agent is at the yellow door facing East. The observation reveals four objects in what appears to be Room 2. Based on the relative descriptions (front/front-left) and distance bins (mid/slightly far), I can estimate local coordinates. "Front" corresponds to local +y, "Left" to local -x. U...

{
  "origin": "agent",
  "objects": {
    "laptop": {
      "position": [
        -2,
        4
      ],
      "facing": "+y"
    },
    "airplane": {
      "position": [
        -3,
        5
      ],
      "facing": "+x"
    },
    "backpack": {
      "position": [
        -1,
        6
      ],
      "facing": "-x"
    },
    "books": {
      "position": [
        0,
        3
      ]
    }
  }
}

{
  "backpack": {
    "position": [
      -2,
      6
    ],
    "facing": "north"
  },
  "laptop": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      -4,
      6
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "laptop": {
      "position": [
        -2,
        4
      ],
      "facing": "+y"
    },
    "airplane": {
      "position": [
        -3,
        5
      ],
      "facing": "+x"
    },
    "backpack": {
      "position": [
        -1,
        6
      ],
      "facing": "-x"
    },
    "books": {
      "position": [
        0,
        3
      ]
    }
  }
}

{
  "backpack": {
    "position": [
      -2,
      6
    ],
    "facing": "north"
  },
  "laptop": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      -4,
      6
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  }
}

THINK: [The agent started in Room 1 (West room) and has performed two observations: one facing North (seeing nothing) and one facing East (seeing the yellow door to the East and blue door to the South). The agent then jumped to the yellow door and observed East into Room 2.
From the initial position (likely near 'L' in the NW corner of Room 1):
- North facing observed the northern strip (candidates D, E, F).
- East facing observed the eastern strip (towards the yellow door).
- The region to the South and South-West of the start position falls outside the North and East fields of view (blind spots). This corresponds to candidates B, G, K, I, H.
- Room 2 (East of the yellow door) was observed after jumping to the door. Candidates C, A, J are in Room 2 and were within the FOV (NE, E, SE).
Therefore, the unexplored candidates are those in the South/South-West of Room 1.]
FINAL ANSWER: {
"unexplored": ["B", "G", "H", "I", "K"]
}

THINK: [The agent started in Room 1 (West room) and has performed two observations: one facing North (seeing nothing) and one facing East (seeing the yellow door to the East and blue door to the South). The agent then jumped to the yellow door and observed East into Room 2.
From the initial position...

################
#########......#
#########DEF...#
##..L...#......#
##..H...#......#
##......#C...A.#
##B.....*...J..#
##.G....########
##K..I..########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You jumped to yellow door. You observe:
• laptop: front-left, slightly far, facing forward
• airplane: front-left, slightly far, facing right
• backpack: front-slight-left, slightly far, facing left
• books: front, mid distance
Assume your current facing direction is called "north":
• laptop is south, near to backpack
• laptop is west, near to books
• airplane is west, near to backpack.
You have a maximum of 17 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to yellow door. You observe:
• laptop: front-left, slightly far, facing forward
• airplane: front-left, slightly far, facing right
• backpack: front-slight-left, slightly far, facing left
• books: front, mid distance
Assume your current facing direction is called "north":
• laptop is sou...

The agent is at the "yellow door" facing East, looking into Room 2. The observation revealed "books" (front, mid distance) and other objects (laptop, airplane, backpack) to the front-left (North-East). The South side of Room 2 is currently unexplored. To efficiently map Room 2, the agent should move into the room and observe the unknown area. Jumping to "books" places the agent centrally or deeper into Room 2. Rotating 90 degrees clockwise (to face South) allows the agent to observe the previously unseen southern part of Room 2.

The agent is at the "yellow door" facing East, looking into Room 2. The observation revealed "books" (front, mid distance) and other objects (laptop, airplane, backpack) to the front-left (North-East). The South side of Room 2 is currently unexplored. To efficiently map Room 2, the agent should move...

THINK:
The agent has successfully navigated from Room 1 to Room 2.
1. **Initial State**: Agent at (0,0) facing North. Observed nothing.
2. **Rotation**: Rotated 90° clockwise to face East. Observed "shoes" (front-slight-right), "rubberduck" (front-right), "alarmclock" (front-left), "yellow door" (front-slight-right, on front wall), "blue door" (front-right, on right wall).
* Estimates (relative to 0,0 facing E):
* Yellow Door (YD): East wall. Roughly (5, 0).
* Blue Door (BD): South wall. Roughly (2, -4).
* Shoes: SE area. (5, -1).
* Rubberduck: SE area. (3, -2).
* Alarmclock: NE area. (3, 2).
3. **Movement**: Jumped to "yellow door" (5, 0). Agent facing East.
* Observed into Room 2: "laptop" (front-left), "airplane" (front-left), "backpack" (front-slight-left), "books" (front).
* Estimates (relative to 5,0 facing E):
* Books: East. Mid distance. (8, 0).
* Laptop (L): NE. West of Books. (7, 2).
* Backpack (BP): NE. North of Laptop. (9, 3).
* Airplane (Air): NE. West of Backpack. (5, 3).
4. **Movement**: Jumped to "books" (8, 0). Rotated 90° clockwise. Agent now at (8, 0) facing South.
* Observed: Nothing. This implies the area South of books is empty or outside FOV boundaries.

Current Map State:
Agent is at (8, 0) facing South.
Objects are placed based on relative observations and constraints.
- Room 1: Shoes, Rubberduck, Alarmclock, Yellow Door, Blue Door.
- Room 2: Laptop, Airplane, Backpack, Books.

The JSON map will reflect these coordinates.

FINAL ANSWER:
```json
{
"agent": {"position": [8, 0], "facing": "south"},
"shoes": {"position": [5, -1], "facing": "west"},
"rubberduck": {"position": [3, -2], "facing": "north"},
"alarmclock": {"position": [3, 2], "facing": "west"},
"yellow door": {"position": [5, 0]},
"blue door": {"position": [2, -4]},
"laptop": {"position": [7, 2], "facing": "east"},
"airplane": {"position": [5, 3], "facing": "south"},
"backpack": {"position": [9, 3], "facing": "north"},
"books": {"position": [8, 0]}
}
```

THINK:
The agent has successfully navigated from Room 1 to Room 2.
1. **Initial State**: Agent at (0,0) facing North. Observed nothing.
2. **Rotation**: Rotated 90° clockwise to face East. Observed "shoes" (front-slight-right), "rubberduck" (front-right), "alarmclock" (front-left), "yellow door" (...

{
  "agent": {
    "position": [
      8,
      0
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      5,
      -1
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      3,
      -2
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      3,
      2
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      5,
      0
    ]
  },
  "blue door": {
    "position": [
      2,
      -4
    ]
  },
  "laptop": {
    "position": [
      7,
      2
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      5,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      9,
      3
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      8,
      0
    ]
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      10,
      -1
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      10,
      -1
    ],
    "facing": "south"
  }
}

THINK:
The agent is currently located at the "books" object, facing South (rotated 90 degrees clockwise from East). The most recent observation reported "No objects in field of view". Therefore, the local cognitive map will contain no observed objects relative to the agent's current frame of reference.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {}
}
```

THINK:
The agent is currently located at the "books" object, facing South (rotated 90 degrees clockwise from East). The most recent observation reported "No objects in field of view". Therefore, the local cognitive map will contain no observed objects relative to the agent's current frame of referen...

{
  "origin": "agent",
  "objects": {}
}

{
  "origin": "agent",
  "objects": {}
}

THINK: [The agent started in Room 1 (Top-Left). It looked North (saw nothing) and East (saw objects and doors). This implies the West and South-West sectors of Room 1 are unobserved. Candidates I, H, K, C, G are located in these blind spots (West and South walls/corners). The agent then moved to Room 2 (Right) and observed East and South. This covers most of Room 2. Candidate A is in the East of Room 2 (covered). Candidate J is in the South-East of Room 2 (likely covered by South or East look). Thus, the unexplored candidates are those in the blind spots of Room 1.]
FINAL ANSWER: {
"unexplored": ["C", "G", "H", "I", "K"]
}

THINK: [The agent started in Room 1 (Top-Left). It looked North (saw nothing) and East (saw objects and doors). This implies the West and South-West sectors of Room 1 are unobserved. Candidates I, H, K, C, G are located in these blind spots (West and South walls/corners). The agent then moved to Roo...

################
#########.....L#
#########.F....#
##.I...D#EB....#
##......#.....A#
##......#.....J#
##......+...*..#
##HK.C..########
##.G....########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You jumped to books. You rotated clockwise 90°. You observe: No objects in field of view..
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to books. You rotated clockwise 90°. You observe: No objects in field of view..
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at "books" in Room 2, facing South. The goal is to exit Room 2 and proceed to Room 3 via the "blue door" in Room 1. To leave Room 2, the agent must jump to the "yellow door". The "yellow door" is to the West of "books" (since "books" are East of the door). The agent is currently facing South. To see the "yellow door", the agent must rotate 90 degrees clockwise to face West. After rotating, the agent will observe to confirm the door is in view for the next jump.

The agent is at "books" in Room 2, facing South. The goal is to exit Room 2 and proceed to Room 3 via the "blue door" in Room 1. To leave Room 2, the agent must jump to the "yellow door". The "yellow door" is to the West of "books" (since "books" are East of the door). The agent is currently facing ...

THINK:
The agent started at (0,0) facing North.
1. **Observe**: Saw nothing.
2. **Rotate(90), Observe**: Facing East.
* **Yellow Door**: Front-slight-right (East-ish), slightly far. On front wall (East wall). Est: (5, 0).
* **Blue Door**: Front-right (South-East), slightly far. On right wall (South wall). Est: (2, -4).
* **Shoes**: Front-slight-right (East-South-East). Near to Rubberduck, South (local West) of Yellow Door. Est: (4, -1). Facing Backward (West).
* **Rubberduck**: Front-right (South-East). East (local South) of Alarmclock. Est: (2, -1). Facing Left (North).
* **Alarmclock**: Front-left (North-East). Est: (2, 1). Facing Backward (West).
3. **JumpTo(yellow door), Observe**: At (5,0) facing East.
* **Books**: Front (East), mid distance. Est: (8, 0).
* **Laptop**: Front-left (North-East). West (local South - wait, "laptop is west, near to books"). West of Books (7,0). South of Backpack. Est: (7, 0). Facing Forward (East).
* **Backpack**: Front-slight-left (East-North-East). North of Laptop. Est: (7, 1). Facing Left (North).
* **Airplane**: Front-left (North-East). West of Backpack. Est: (6, 1). Facing Right (South).
4. **JumpTo(books), Rotate(90), Observe**: At (8,0) facing South. Saw nothing.
5. **Rotate(90), Observe**: At (8,0) facing West.
* **Yellow Door**: Front (West), mid distance. Consistent with (5,0).

FINAL ANSWER:
```json
{
"agent": {"position": [8, 0], "facing": "west"},
"yellow door": {"position": [5, 0]},
"blue door": {"position": [2, -4]},
"shoes": {"position": [4, -1], "facing": "west"},
"rubberduck": {"position": [2, -1], "facing": "north"},
"alarmclock": {"position": [2, 1], "facing": "west"},
"books": {"position": [8, 0]},
"laptop": {"position": [7, 0], "facing": "east"},
"backpack": {"position": [7, 1], "facing": "north"},
"airplane": {"position": [6, 1], "facing": "south"}
}
```

THINK:
The agent started at (0,0) facing North.
1. **Observe**: Saw nothing.
2. **Rotate(90), Observe**: Facing East.
* **Yellow Door**: Front-slight-right (East-ish), slightly far. On front wall (East wall). Est: (5, 0).
* **Blue Door**: Front-right (South-East), slightly far. On righ...

{
  "agent": {
    "position": [
      8,
      0
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      5,
      0
    ]
  },
  "blue door": {
    "position": [
      2,
      -4
    ]
  },
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "books": {
    "position": [
      8,
      0
    ]
  },
  "laptop": {
    "position": [
      7,
      0
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      7,
      1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      6,
      1
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      10,
      -1
    ],
    "facing": "west"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      10,
      -1
    ],
    "facing": "west"
  }
}

THINK:
1. **Current State**: Agent is at "books" in Room 2. The agent just rotated to face West (relative to global North, or local "front").
2. **Observation**: The agent sees "yellow door" at "front, mid distance".
* Distance bin "mid distance": (2, 4]. Let's estimate distance = 3.
* Direction "front": (0 degrees).
* Local coordinates: Front is +y. So, relative position is approx (0, 3).
* Orientation of door: "on front wall". Since the agent is facing the door (West), the door is on the West wall of Room 2. However, the observation says "on front wall" relative to the agent's view. If the agent faces the door, the door plane is perpendicular to the view direction. Usually, doors are represented as connecting points. If the door is on the "front wall" from the agent's perspective, it means the agent is looking at the wall. The door's "facing" isn't typically defined like an object, but rather its location. The schema asks for position and facing if applicable. Doors usually don't have a "facing" property in the same way objects do (like "facing left"), but here it says "on front wall". Let's omit "facing" for the door unless it implies an object-like orientation, or use the wall normal. The prompt says "Gate's orientation: report wall position". The JSON schema asks for "facing" if the object has one. The previous observations for objects had "facing backward", etc. The door observation says "on front wall". I will include the position.
* Relative Position: (0, 3) (Front = +y).
* Let's check the previous step. The agent was at "yellow door" facing East and jumped to "books" (front, mid distance). So "books" is roughly (0, 3) relative to the door (facing East). Now the agent is at "books" facing West. The door should be at (0, 3) relative to the agent.
3. **Construct JSON**:
* Origin: "agent".
* Object: "yellow door".
* Position: [0, 3] (approx). Since "mid distance" is (2,4], 3 is a good integer proxy.
* Facing: The observation says "on front wall". In the local frame (+y is forward/West), the wall is at +y. A door on that wall faces -y (into the room) or +y (out of the room). Let's stick to the observed attributes. The schema asks for "+x|-x|+y|-y". "on front wall" implies the surface normal faces the agent (-y) or is aligned with the wall (x axis). However, usually for doors we just need the location. I will provide the position. If I must provide facing, "facing backward" relative to the agent would be -y. But the raw observation is "on front wall". I will omit facing for the door to be safe, or make a best guess. Actually, looking back at the prompt's examples or instructions: "Include only observed objects... MUST include facing key if the object has facing direction." The door observation doesn't explicitly say "facing X" like "facing backward", it says "on front wall". I will omit the facing key for the door.

Wait, looking at the previous observation of objects: "shoes: ... facing backward".
This observation: "yellow door: ... on front wall".
It seems "on front wall" is the orientation description for the door. I shouldn't try to map it to a direction vector unless confident. I will omit "facing" for the door in the JSON as it's not a standard cardinal direction relative to the agent provided in the "facing X" format.

Refining position: "mid distance" is >2 and <=4. Let's use 3.
Local +y is "front". So [0, 3].

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"yellow door": {"position": [0, 3]}
}
}

THINK:
1. **Current State**: Agent is at "books" in Room 2. The agent just rotated to face West (relative to global North, or local "front").
2. **Observation**: The agent sees "yellow door" at "front, mid distance".
* Distance bin "mid distance": (2, 4]. Let's estimate distance = 3.
* ...

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        0,
        3
      ]
    }
  }
}

{
  "yellow door": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        0,
        3
      ]
    }
  }
}

THINK: [The agent started in Room 1, facing North. It observed North (saw nothing), then rotated to face East and observed (saw objects and doors). It then jumped to the Yellow Door and observed Room 2 (facing East), seeing objects in the North-East. Finally, it jumped to 'books' in Room 2 and rotated South (saw nothing) and then West (saw door).
Based on the observations:
Room 1:
- North facing observed the North sector.
- East facing observed the East and South-East sectors (FOV +/- 45 degrees).
- The West (H) and South-West (E, B) sectors were never observed. B is likely outside the South-East cone (angle > 45 deg from East).
- J is likely on the edge or inside the SE cone (45 deg). Given B and E are likely blind, B and E are candidates. H is definitely blind.
- D is North-West. From North facing, D is likely inside the FOV (angle < 45 deg). So D is observed.
Room 2:
- From Yellow Door (facing East), the agent saw the North-East sector.
- L and F are in the North/North-North-East sector, likely outside the 45-degree FOV from the door.
- K is in the North-East, likely inside the FOV (observed objects there).
- The agent looked South from 'books', clearing the South sector (I is also seen from the door).
- Therefore, F and L are unobserved.

Unexplored candidates: B, E, F, H, L.]
FINAL ANSWER: {
"unexplored": ["B", "E", "F", "H", "L"]
}

THINK: [The agent started in Room 1, facing North. It observed North (saw nothing), then rotated to face East and observed (saw objects and doors). It then jumped to the Yellow Door and observed Room 2 (facing East), seeing objects in the North-East. Finally, it jumped to 'books' in Room 2 and rotat...

################
#########.FK...#
#########L.....#
##.D....#...A..#
##......#......#
##......#.I....#
##H.G...+C..*..#
##.EJ...########
##..B...########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You rotated clockwise 90°. You observe:
• yellow door: front, mid distance, on front wall.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• yellow door: front, mid distance, on front wall.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at "books" facing West and sees the "yellow door" ahead. The plan is to return to Room 1 and then go to Room 3 through the "blue door".
1. Jump to "yellow door". This places the agent back at the boundary between Room 1 and Room 2.
2. The agent's orientation is West. From the "yellow door", facing West looks back into Room 1.
3. The "blue door" was previously observed in Room 1. The agent was at (0,0) facing East when it saw the "blue door" on the right wall (South). This means the "blue door" is roughly South-East from the origin. The "yellow door" is roughly East from the origin. Therefore, the "blue door" is likely to the South or South-West relative to the "yellow door".
4. From the "yellow door" facing West, South is to the left.
5. To see the "blue door" from the "yellow door" position inside Room 1, the agent needs to face towards it. If the "blue door" is on the South wall of Room 1 and the "yellow door" is on the East wall, then looking from the "yellow door" into Room 1 (West), the "blue door" would be on the left (South).
6. Therefore, after jumping to the "yellow door", the agent should rotate -90 degrees (counter-clockwise) to face South. This should bring the "blue door" into the field of view.

The agent is at "books" facing West and sees the "yellow door" ahead. The plan is to return to Room 1 and then go to Room 3 through the "blue door".
1. Jump to "yellow door". This places the agent back at the boundary between Room 1 and Room 2.
2. The agent's orientation is West. From the "yellow ...

THINK:
1. **Analyze current state:** The agent is at the `yellow door`, facing South.
2. **Recall observations and positions:**
* **Initial:** Agent at [0, 0], facing North. Observed nothing.
* **Turn 1:** Rotated 90° clockwise. Facing East. Observed:
* `shoes`: front-slight-right, slightly far (~5 units), facing backward (West).
* `rubberduck`: front-right, mid distance (~3 units), facing left (North).
* `alarmclock`: front-left, mid distance (~3 units), facing backward (West).
* `yellow door`: front-slight-right, slightly far (~5 units), on front wall.
* `blue door`: front-right, slightly far (~5 units), on right wall.
* **Inferred Positions (Room 1):**
* Agent facing East (axis +x).
* `yellow door`: East, slightly South? "front-slight-right". Let's approximate. East is +x. Front is +x. Slight right is towards -y. So maybe [5, -1]?
* `blue door`: Front-right. East + South. Roughly South-East. "on right wall" implies it's on the South wall. Maybe [3, -5]?
* `shoes`: Front-slight-right. Near yellow door.
* `rubberduck`: Front-right.
* `alarmclock`: Front-left. East + North. Maybe [3, 2]?
* **Action 2:** Jumped to `yellow door`. Facing East. Observed Room 2.
* `laptop`: front-left (North-East).
* `airplane`: front-left.
* `backpack`: front-slight-left.
* `books`: front (East), mid distance (~3 units).
* **Inferred Positions (Room 2):**
* Agent at `yellow door` position. Let's fix `yellow door` at [5, 0] for simplicity (pure East) given "front wall" from (0,0) facing East usually implies x-axis alignment, though "slight-right" suggests y < 0. Let's stick to integer coordinates. If (0,0) facing East sees yellow door "front-slight-right", and distance is "slightly far" (4-8), let's say dx=5, dy=-1 or -2. Let's assume [5, -1].
* From `yellow door` [5, -1] facing East:
* `books`: Front (East), mid distance (2-4). Position: [5+3, -1] = [8, -1].
* `laptop`, `airplane`, `backpack`: North-East.
* **Action 3:** Jumped to `books`. Rotated 90° clockwise (facing South). Observed nothing.
* Agent at [8, -1], facing South.
* **Action 4:** Rotated 90° clockwise (facing West). Observed `yellow door`.
* Agent at [8, -1], facing West. `yellow door` is front (West), mid distance (3 units). Consistent.
* **Action 5:** Jumped to `yellow door`. Rotated 90° counter-clockwise (facing South). Observed `blue door` front-right, mid distance.
* Agent at `yellow door` [5, -1], facing South.
* `blue door`: Front-right. Front is South (-y). Right is West (-x). So South-West relative to yellow door.
* Wait, previous observation of `blue door` from (0,0) facing East was "front-right" (South-East).
* From `yellow door` [5, -1] facing South: "front-right" means South (-y) and West (-x).
* Let's refine coordinates.
* Start (0,0). `yellow door` is East-ish. `blue door` is South-East-ish.
* `yellow door` pos: [5, -1].
* `blue door` pos relative to [5, -1] facing South: Front (South) + Right (West). Vector (-x, -y). So x < 5, y < -1.
* Mid distance (2-4). E.g., dx=-2, dy=-2. Pos: [3, -3].
* Check against origin view (0,0) facing East: `blue door` at [3, -3] would be East (+3) and South (-3). Angle from East is -45 degrees (South-East). Matches "front-right" bin (22.5 to 67.5 degrees to the right). Correct.
* `books` pos: [8, -1].
* `laptop`: From `yellow door` (facing East), it was "front-left" (North-East). Say [8, 2].
* `airplane`: "front-left". Say [9, 1].
* `backpack`: "front-slight-left". Say [9, 0].
* `shoes`: From (0,0) facing East, "front-slight-right" (East-South). Near `yellow door`. Say [4, -1].
* `rubberduck`: From (0,0) facing East, "front-right". Say [3, -2].
* `alarmclock`: From (0,0) facing East, "front-left" (East-North). Say [3, 2].

3. **Construct JSON:**
* Agent: At `yellow door`, facing South. Pos: [5, -1].
* `yellow door`: [5, -1]. Facing West (into Room 1) or East (into Room 2)? Doors connect rooms. Let's assume the coordinate is the gateway. Facing isn't strictly applicable like objects, but the prompt asks for observed objects and gates. I'll include position. Facing? The door itself is "on front wall" (East wall of Room 1).
* `blue door`: [3, -3]. Facing North (into Room 1)? It's on the "right wall" (South wall) when facing East. So it faces North.
* `books`: [8, -1]. Facing? Not specified in observation, usually. Wait, first observation of books: "facing" not mentioned? Ah, "facing" key is required *if the object has facing direction*. Re-read observation 2: "books: front, mid distance". No facing mentioned. Re-read observation 1: "shoes... facing backward".
* `shoes`: [4, -1]. Facing West ("backward" relative to East view).
* `rubberduck`: [3, -2]. Facing North ("left" relative to East view).
* `alarmclock`: [3, 2]. Facing West ("backward" relative to East view).
* `laptop`: [8, 2]. Facing West ("forward" relative to East view? No, "facing forward" relative to agent facing East means facing East? Or facing the agent? "facing forward" usually means the object's front is aligned with the agent's view direction. Agent facing East -> Object facing East. Let's check definitions. "forward/backward/right/left (ego)... When agent faces north: forward = north". So "facing forward" means the object's orientation is the same as the agent's current ego-forward. Agent faces East. Object faces East.
* `airplane`: [9, 1]. Facing South ("right" relative to East view).
* `backpack`: [9, 0]. Facing North ("left" relative to East view).

*Refining positions based on "Near" relations:*
* `shoes` near `yellow door`. [4, -1] and [5, -1] is dist 1. Good.
* `rubberduck` near `alarmclock`? [3, -2] and [3, 2] is dist 4. Maybe too far for "near" (<=2). Let's adjust.
* Obs 1: "rubberduck is east, near to alarmclock". This is a relative report. "east" means rubberduck is East of alarmclock? Or in the East direction from the agent? "Assume your current facing direction is called 'north'". Agent faces East (real world). So "north" map = East real. "rubberduck is east" in map frame -> South in real world relative to alarmclock? No, this relative text is confusing.
* Let's stick to egocentric bins.
* Obs 1: Agent (0,0) facing East.
* `alarmclock`: front-left (East-North). e.g. [3, 2].
* `rubberduck`: front-right (East-South). e.g. [3, -2].
* Distance [3, 2] to [3, -2] is 4. "Near" is <= 2.
* Maybe `alarmclock` is [3, 1] and `rubberduck` is [3, -1]? Distance 2. Fits "mid distance" (2,4] from origin (dist 3.16). Fits "front-left" and "front-right".
* Obs 2: Agent at `yellow door` [5, -1] facing East.
* `laptop`: front-left (East-North).
* `backpack`: front-slight-left.
* `books`: front. [8, -1].
* `laptop` near `backpack`.
* `laptop` near `books`.
* `airplane` near `backpack`.
* Let's cluster them. `books` at [8, -1].
* `laptop` near `books`: [8, 0]?
* `backpack`: [7, 0]?
* `airplane`: [6, 1]?
* Check bins:
* `laptop` from [5,-1]: vector [3, 1]. Angle atan(1/3) ~ 18 deg. Front-slight-left (0 to 22.5). Obs says "front-left" (22.5 to 45). Maybe `laptop` is [8, 2]. Vector [3, 3], angle 45. Too much. [7, 1] vector [2, 2], 45 deg. [7, 2] vector [2, 3], 56 deg.
* Let's guess `laptop` at [8, 1]. Vector [3, 2]. Angle ~33 deg. Fits "front-left". Dist sqrt(13) ~ 3.6 (mid, or slightly far? Obs says "slightly far" (4,8]). 3.6 is "mid". Need further.
* Let's push `yellow door` further to satisfy "slightly far" (>4) from origin.
* Say `yellow door` is at [6, 0].
* Agent at [6, 0].
* `books` mid distance (2-4). Say at [9, 0] (dist 3).
* `laptop` slightly far (>4). Say [10, 3]. Vector [4, 3], dist 5. Angle ~37 deg (front-left). Fits.
* `backpack` slightly far (>4). Say [10, 1]. Vector [4, 1], dist 4.1. Angle ~14 deg (front-slight-left). Fits.
* `airplane` slightly far. Front-left. Say [9, 3]. Vector [3, 3], dist 4.2. Angle 45 deg. Fits.
* Recalculate Room 1 with `yellow door` at [6, 0].
* Origin (0,0). `yellow door` at [6, 0] is distance 6 (slightly far). Angle 0 (front). Obs: "front-slight-right". So y is negative. [6, -1]. Dist ~6. Angle small right. Fits.
* `shoes`: near `yellow door`. [5, -1]. Slightly far from origin? Dist ~5. Fits.
* `blue door`: slightly far. Front-right. Say [4, -4]. Dist ~5.6. Angle -45. Fits.
* `alarmclock`: front-left. Mid distance (2-4). Say [3, 1]. Dist 3.16. Angle ~18 deg (front-slight-left). Obs says "front-left". Needs > 22.5 deg. Say [2, 2]. Dist 2.8. Angle 45. Fits.
* `rubberduck`: front-right. Mid distance. Say [2, -2]. Dist 2.8. Angle -45. Fits.
* Relative: `shoes` near `rubberduck`? [5, -1] vs [2, -2]. Dist 3.16. Not near (>2). Maybe rubberduck is [3, -1]? Dist from origin 3.16. Angle -18 (front-slight-right). Obs says "front-right". Needs > 22.5. So y must be more negative or x smaller.
* This is an approximation task. I will generate a consistent set of integer coordinates.

*Proposed Coordinates:*
* Agent (Start): [0, 0]
* Agent (Current): `yellow door` pos.
* `yellow door`: [6, -1]
* `blue door`: [4, -4] (Front-right from origin. From yellow door [6,-1] facing South, it's [4,-4] -> vector [-2, -3]. Forward is -y. Right is -x. It is forward 3, right 2. "Front-right". Dist 3.6 (mid). Matches.)
* `shoes`: [5, -2] (Near yellow door. From origin: Front-slight-right. Dist 5.3. Slightly far. Matches.)
* `rubberduck`: [3, -3] (From origin: Front-right. Dist 4.2. Slightly far? Obs says "mid". Maybe [2, -2]. Dist 2.8. Matches.)
* `alarmclock`: [2, 2] (From origin: Front-left. Dist 2.8. Mid. Matches.)
* `books`: [9, -1] (From yellow door [6, -1]: Front (East). Dist 3. Mid. Matches.)
* `laptop`: [9, 2] (From yellow door: Front-left. Dist 4.2. Slightly far. Matches.)
* `airplane`: [8, 2] (From yellow door: Front-left. Dist 3.6. Mid? Obs: "slightly far". Maybe [9, 3].)
* `backpack`: [10, 0] (From yellow door: Front-slight-left. Dist 4.1. Slightly far. Matches.)

*Facings:*
* Agent: South
* `shoes`: West (backward to East)
* `rubberduck`: North (left to East)
* `alarmclock`: West (backward to East)
* `laptop`: East (forward to East)
* `airplane`: South (right to East)
* `backpack`: North (left to East)
* `books`: Not specified, omit.

FINAL ANSWER:
```json
{
"agent": {"position": [6, -1], "facing": "south"},
"yellow door": {"position": [6, -1]},
"blue door": {"position": [4, -4]},
"shoes": {"position": [5, -2], "facing": "west"},
"rubberduck": {"position": [2, -2], "facing": "north"},
"alarmclock": {"position": [2, 2], "facing": "west"},
"books": {"position": [9, -1]},
"laptop": {"position": [9, 2], "facing": "east"},
"airplane": {"position": [9, 3], "facing": "south"},
"backpack": {"position": [10, 0], "facing": "north"}
}
```

THINK:
1. **Analyze current state:** The agent is at the `yellow door`, facing South.
2. **Recall observations and positions:**
* **Initial:** Agent at [0, 0], facing North. Observed nothing.
* **Turn 1:** Rotated 90° clockwise. Facing East. Observed:
* `shoes`: front-slight-...

{
  "agent": {
    "position": [
      6,
      -1
    ],
    "facing": "south"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ]
  },
  "blue door": {
    "position": [
      4,
      -4
    ]
  },
  "shoes": {
    "position": [
      5,
      -2
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -2
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "books": {
    "position": [
      9,
      -1
    ]
  },
  "laptop": {
    "position": [
      9,
      2
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      9,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      10,
      0
    ],
    "facing": "north"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      -1
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      -1
    ],
    "facing": "south"
  }
}

THINK:
The agent is currently at the "yellow door" facing South (global frame).
The "blue door" is observed at front-right, mid distance.
In the local frame:
- The agent is at (0,0).
- Facing forward is +y.
- Right is +x.
- "front-right" implies positive x and positive y.
- "mid distance" corresponds to (2, 4]. Let's estimate local coordinates [2, 3].
- The "blue door" is "on front wall". In the global frame, the agent faces South. The "front wall" relative to the agent is the South wall. The door is on this wall.
- The door's orientation is usually perpendicular to the wall. If the wall is "front" (relative to agent facing +y), the wall is parallel to the x-axis. A door on this wall faces the agent (or away). So facing is typically opposed to the agent or aligned. Let's assume standard door representation where facing indicates the normal out of the wall into the room, or vice-versa. The prompt says "on front wall". Let's denote its facing. If the agent faces South (+y local), and the door is on the front wall, the door faces North (-y local) into the room.

Wait, let's refine coordinates based on "front-right".
Distance is mid (say 3m). Angle is front-right (22.5 to 45 degrees).
Let's approximate: x=2, y=3 gives angle arctan(2/3) ~ 33 deg, dist sqrt(13) ~ 3.6. Fits.
Or x=1, y=3 gives arctan(1/3) ~ 18 deg (front-slight-right).
Or x=3, y=3 gives 45 deg.
Let's pick integers that fit "mid distance" and "front-right".
The prompt says "front-right" is (22.5, 45].
If dist is ~3.
x=1, y=3 -> dist 3.16, angle 18.4 (too small).
x=2, y=3 -> dist 3.6, angle 33.7 (good).
x=2, y=2 -> dist 2.8, angle 45 (boundary).
Let's use [2, 3] for local coordinates.

Facing of the blue door:
Agent is facing South. Door is on "front wall" (South wall).
Doors usually face into the room. So the door faces North.
In local frame (North is -y relative to agent? No, agent faces South. So South is +y local. North is -y local).
So door facing is "-y" in local frame.

Let's verify "on front wall".
If I face +y, front wall is at some +y coordinate. The door is embedded in it.
So the door's normal is along the y-axis. It faces -y (towards me).

Final check:
Agent at yellow door. Facing South.
Blue door is to the South-West of the yellow door in global coordinates?
Wait, previous observation from (0,0) facing East:
Yellow door: front-slight-right (East-South-ish).
Blue door: front-right (South-East-ish).
If yellow door is at (E, S1) and blue is at (E2, S).
This geometry is getting complicated.
Let's stick to the local observation.
"blue door: front-right, mid distance, on front wall."
Local frame: origin=agent.
Object: "blue door".
Position: [2, 3] (approx for front-right, mid dist).
Facing: "-y" (on front wall, facing back to agent).

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"blue door": {"position": [2, 3], "facing": "-y"}
}
}

THINK:
The agent is currently at the "yellow door" facing South (global frame).
The "blue door" is observed at front-right, mid distance.
In the local frame:
- The agent is at (0,0).
- Facing forward is +y.
- Right is +x.
- "front-right" implies positive x and positive y.
- "mid distance" correspon...

{
  "origin": "agent",
  "objects": {
    "blue door": {
      "position": [
        2,
        3
      ],
      "facing": "-y"
    }
  }
}

{
  "blue door": {
    "position": [
      2,
      3
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "blue door": {
      "position": [
        2,
        3
      ],
      "facing": "-y"
    }
  }
}

THINK:
The agent started at (0,0) (let's assume relative to the map visualization, the map coordinates provided in the text description differ from the fog probe map which uses a grid visualization).
Let's analyze the Fog Probe Map.
The map shows walls ('#'), doors ('+'), and the agent's position ('*').
The agent is currently at the "yellow door". Looking at the map, there is a '+' symbol at the junction of two rooms. However, the agent's position '*' is shown in the room on the left, near a wall gap leading to the room on the right.
Wait, let's re-read the context. The agent is at the "yellow door".
In the map provided:
There is a room on the left (Room 1 presumably, based on the shape and connections) and a room on the right (Room 2).
The agent '*' is located at a doorway connecting the left room to the right room.
Wait, the '*' is at `x=8, y=7` (approx, counting from bottom-left 0,0).
Let's trace the agent's path:
1. Start Room 1 (0,0).
2. Saw yellow door (East) and blue door (South).
3. Jumped to yellow door. Now at yellow door.
4. Jumped to books (Room 2).
5. Jumped back to yellow door.
Current position: Yellow door.
Orientation: South (agent rotated -90 from West).

Map analysis:
The map shows three main areas:
- A large room on the left (Room 1).
- A room on the right (Room 2).
- A room below Room 1 (Room 3, accessed via the door at the bottom of Room 1).

The agent is at '*'.
Candidates:
A: In Room 1, West of the agent. This area was traversed/observed? The agent started at (0,0) and looked East. Then rotated and looked East again? No, started North (saw nothing), then East (saw doors), then jumped to yellow door. The area A is in the middle of Room 1. Since the agent looked East from (0,0) and saw the yellow door, the FOV covers the cone from (0,0) towards East. Point A is likely inside Room 1. Is it unobserved? The initial observation was North (empty). The second was East (saw objects). A is likely in the central part of Room 1.
B: In Room 2 (top right). Agent went to 'books'. Where are 'books'? The agent was at yellow door looking East, saw books front (mid distance). Jumped to books. Rotated South (saw nothing). B is North of the 'books' position (presumably). The agent has not looked North in Room 2. So B is likely unexplored.
C: In Room 2, near the center. Agent was at books and looked South. C looks close to where books might be or just West of it.
D: In Room 2, South part. Agent looked South from books. Saw nothing. This implies the area South of books is empty or the wall is there. But D is shown in the open space. If the agent saw nothing, it means no *objects*, but the space itself was "seen" (cleared fog)? The question asks for points in "unexplored/unobserved regions". Usually, this means areas outside the FOV cones generated so far.
E: In Room 2, East side.
F: In Room 1, South-West.
G: In Room 2, North side. Unobserved.
H: In Room 1, West wall.
I: In Room 2, North-East.
J: In Room 1, West side.
K: In Room 1, North-West.
L: In Room 1, near the yellow door.

Let's refine based on FOV history.
1. Pos=(0,0) Room 1. Facing North. FOV=North. Saw nothing. (Region North of start).
2. Pos=(0,0) Room 1. Facing East. FOV=East. Saw Yellow Door, Blue Door, Shoes, Rubberduck, Alarmclock. (Region East of start).
3. Pos=Yellow Door. Facing East. FOV=East into Room 2. Saw Laptop, Airplane, Backpack, Books.
4. Pos=Books. Facing South. FOV=South. Saw nothing.
5. Pos=Books. Facing West. FOV=West. Saw Yellow Door.
6. Pos=Yellow Door. Facing South. FOV=South. Saw Blue Door.

Let's map the candidates to the grid.
Room 1 is the left region.
Room 2 is the right region.
Room 3 is the bottom region (below the '+' at the bottom).

Room 1 Coverage:
- Agent at (0,0) looked North. Cover strip North of (0,0).
- Agent at (0,0) looked East. Cover strip East of (0,0).
- Agent at Yellow Door looked South into Room 1 (current step). Covers area South of Yellow Door.

Room 2 Coverage:
- Agent at Yellow Door looked East. Covers central strip of Room 2.
- Agent at Books looked South. Covers South strip of Room 2.
- Agent at Books looked West. Covers strip back to door.

Unexplored areas:
Room 1:
- West side/North-West? Agent was at (0,0) (bottom-left of Room 1? or center?). The text says "treat your initial position as the origin (0, 0)". The map shows the connection to Room 3 (bottom door) is at the bottom. The connection to Room 2 (yellow door) is on the right.
If (0,0) is in Room 1, and the yellow door is East, and blue door is South (wait, blue door was on right wall when facing East... so South).
So (0,0) is roughly North-West of the blue door and West of the yellow door.
Looking North from (0,0): Saw nothing.
Looking East from (0,0): Saw Yellow Door.
Candidates H, J, K are on the West side of Room 1. If (0,0) is central, West might be behind. If (0,0) is West, then North covers K?
Let's assume standard layout interpretation.
Candidates in Room 2 (Right Room):
- B, G, I: North part of Room 2. Agent looked East (middle) and South (bottom). North part is likely UNEXPLORED.
- C, E: Middle part. "Books" was found here. Agent jumped to Books and looked West. This area is likely OBSERVED.
- D: South part. Agent looked South from Books. Likely OBSERVED.

Candidates in Room 1 (Left Room):
- L: Near yellow door. Agent has been there. Observed.
- A: Central. Agent looked East through here. Likely Observed.
- F: South-Central. Agent looked South from Yellow door? Yes, just now.
- H, J: West/South-West. Agent started at (0,0). If (0,0) is near F/A, looking North covers L/K? Looking East covers A/L.
Wait, let's look at the map agent marker '*'. It is at the yellow door position.
The coordinates of '*' are approximately (8, 6) relative to bottom-left of the ASCII map block.
Room 1 extends from x=0 to x=7.
Room 2 extends from x=9 to x=15.
Room 3 is below y=9? No, the map is y-up.
The '+' at the bottom is at x=6, y=9 (from top). No, y points up.
Let's parse map rows.
Row 0 (bottom): ################
Row 1: #......######### (Room 3?)
...
Row 6: ######+######### (Door to Room 3?)
Row 7: ##..F...########
Row 8: ##HJ..A.########
Row 9: ##......*.D....# (* is agent at Yellow Door)
Row 10: ##....L.#......#
Row 11: ##......#C.E...#
Row 12: ##K.....#......#
Row 13: #########..I...#
Row 14: #########.GB...#
Row 15: ################

Agent '*' is at x=8, y=6 (0-indexed from bottom, row 9 from top).
Actually, let's count '.' from bottom.
Rows 1-6 are Room 3 (bottom left, connected by +).
Row 7 starts Room 1 (left) and Room 2 (right).
Wait, the '+' at row 6 connects Room 1 (above) and Room 3 (below).
Room 1 is rows 7-12 (approx).
Room 2 is rows 7-14 (approx), connected to Room 1 at x=8 (where '*' is).

Agent History:
1. Start in Room 1.
2. Looked North.
3. Looked East.
4. Went to Yellow Door (*).
5. Went to Room 2 (Books). Looked South.
6. Went back to Yellow Door (*). Looked South.

Room 2 (Right):
- Agent stood at Yellow Door (*) and looked East (Row 9, 10, 11 direction). Covered C, E? "Books" found.
- Agent went to Books (approx C/E area) and looked South. Covered D area.
- Agent has NOT looked North in Room 2.
- Candidates G, B, I are in the North part of Room 2. They are UNEXPLORED.

Room 1 (Left):
- Agent started at (0,0) in Room 1. Let's assume (0,0) is somewhere in the open space.
- Agent looked North.
- Agent looked East.
- Candidates K is in North-West corner.
- Candidates H, J are in South-West corner.
- Candidate F is in South-Central.
- Candidate A is Central.
- Candidate L is North-Central.

Agent is at '*' facing South.
Current view (South from *) sees "Blue Door". Blue door is the '+' at Row 6?
Yes, looks like it.
So the agent sees the area between '*' and the Blue Door. That covers F? Maybe.
What about H, J? They are far West. If agent is at '*' (East wall of Room 1) looking South, the FOV is a cone South. It might not see the South-West corner (H, J).
What about K? North-West. Agent started somewhere and looked North. If start was near A, looking North covers L. Does it cover K?
Let's consider the "Start Position".
Agent at start looked East and saw Yellow Door (slightly far) and Blue Door (slightly far).
Yellow Door is at (8,6) (relative map grid).
Blue Door is at (6,3) (relative map grid, the '+' at bottom).
If Yellow is East and Blue is South-East (from start), the start position must be West of Yellow and North of Blue? No.
Start Facing North.
Rotate 90 -> Facing East.
Saw Yellow (East). Saw Blue (Right -> South).
If facing East, Blue is on Right (South).
So Start is West of Yellow and North of Blue.
Let's say Start is at (4, 6).
Look North: Covers (4,6) to (4,12). K is at (2,12). might be missed if FOV is 90 deg.
Look East: Covers (4,6) to (8,6). Saw Yellow Door. Saw Blue Door (distance?).
Candidates:
Room 2 North (G, B, I) is definitely unexplored.
Room 1 West/North-West (H, J, K). Start pos was likely central. Looking North and East leaves West and South-West blind spots?
Wait, if I am at (x,y) and look East, I see East.
If I look North, I see North.
West and South-West are behind.
So H, J (South West) and K (North West, if not covered by North view) are potential.
However, K is "North-West". If I look North from Center, I see a cone. (x,y) to (x-d, y+d) and (x+d, y+d). K might be seen.
But H and J are South-West. Agent looked North then East. Never looked West or South in Room 1.
So H and J are likely UNEXPLORED.
G, B, I are definitely UNEXPLORED (Room 2 North).

Let's refine K.
Start pos approx (4,6).
Look North: Cone -45 to +45 deg.
(4,6) -> (4,12). Cone width increases.
K is at (2,12). Delta x = -2, Delta y = +6. Angle = arctan(-2/6) = -18 deg. Inside +/- 45 deg cone.
So K is likely observed.

Let's refine H, J.
Start pos (4,6).
H, J are at approx (2,8)? No, map:
Row 8: ##HJ..A.########
H, J are at x=2,3. y=8?
Wait, y counts up. Row 8 is y=8 (if bottom is 0).
Start (4,6).
H, J are West/North-West of Start?
If Start is (4,6), and H,J are at (2,8), they are NW.
Angle to (2,8) from (4,6): dx=-2, dy=+2. Angle 135 deg (North West).
North FOV: [-45, 45]. 135 is outside.
East FOV: [45, 135]? No, East is 0 relative to East. North is 90 relative to East.
East FOV (Global East): [-45, 45] relative to East -> [East-45, East+45] -> [NE, SE].
North FOV (Global North): [NW, NE].
Actually, "Egocentric angle bins (0° is front): [-45°...45°]".
Facing North: See NW to NE.
Facing East: See NE to SE.
So NW (angle 135 deg from East, or -45 from North) is on the edge.
However, H and J are at row 8. Start at row 6?
Let's check the map coordinates again.
Row 9 has '*'.
Row 8 has H, J.
So H, J are South of *.
If Start was West of *, say (4,6). (Row 9 in map is y=6? No map rows go top down in text usually, but "North is Up" label).
Let's assume the ASCII map corresponds to the grid.
Top row is North.
Agent * is at Row 9 (from top). Let's call this Y_agent.
Yellow Door is at *.
Blue door + is at Row 6 (from bottom)? No, Row 15 is bottom.
Let's number rows 0 to 15 from TOP to BOTTOM.
0: #
...
6: ##..F... (No, F is lower?)
Let's look at the labels in the map snippet.
Line 7: ##HJ..A.########
Line 8: ##..F...########
Line 9: ######+######### (Blue door)
Line 6 (above 7): ##......*.D....#
Wait, '*' is on Line 6?
No, looking at the provided map text:
Row 0: ################
Row 1: #########.GB...# (Room 2 North)
Row 2: #########..I...#
Row 3: ##K.....#......# (Room 1 North)
Row 4: ##......#C.E...#
Row 5: ##....L.#......#
Row 6: ##......*.D....# (Agent at Yellow Door)
Row 7: ##HJ..A.######## (Room 1 South?)
Row 8: ##..F...########
Row 9: ######+######### (Blue Door)
Row 10-15: Room 3.

Okay, interpretation:
North is Up (Row 0).
Room 2 (Right) is Rows 1-6.
Room 1 (Left) is Rows 3-9.
Agent * is at Row 6, Col 8. (Yellow Door).
Blue Door + is at Row 9, Col 6.

Agent History:
1. Start in Room 1. Saw North (Empty). Saw East (Yellow Door, Blue Door).
- Yellow Door is at (8, 6).
- Blue Door is at (6, 9).
- Agent saw Yellow (East) and Blue (South-ish?).
- If Agent was at, say, (4, 6) facing East: Yellow is East. Blue is South-East (dx=2, dy=3 down). Correct.
- Initial Pos approx (4, 6).
- Action 1: Look North (Up).
- Pos (4,6). Cone Up. Covers (4,6) to (4,3). Width expands.
- K is at Row 3, Col 2.
- dx = -2, dy = -3 (Up is negative row index).
- Vector (-2, -3). Angle relative to North (0, -1)?
- North vector is (0, -1). Point vector (-2, -3).
- Angle: atan2(-2, -3) vs atan2(0, -1).
- (-2, -3) is roughly North-West.
- FOV is +/- 45 deg.
- Angle of (-2, -3) is roughly 33 deg West of North. Inside FOV.
- **K is OBSERVED.**
- Action 2: Look East (Right).
- Pos (4,6). Cone Right.
- Covers A (Row 7, Col 6)?
- Vector (2, 1) (Right 2, Down 1). Angle approx 26 deg South of East. Inside FOV.
- **A is OBSERVED.**
- Covers L (Row 5, Col 6)?
- Vector (2, -1) (Right 2, Up 1). Angle approx 26 deg North of East. Inside FOV.
- **L is OBSERVED.**
- Covers H, J (Row 7, Col 2, 3)?
- Vector (-2, 1) / (-1, 1). This is South-West / West.
- Outside East FOV.
- Outside North FOV (which is Up).
- **H, J are UNEXPLORED.**
- Covers F (Row 8, Col 4)?
- Vector (0, 2). South.
- Outside East FOV.
- **F is UNEXPLORED** (by initial looks).
- But wait, current action?
- Agent went to Yellow Door (*, Row 6, Col 8).
- Looked South (Down).
- Pos (8, 6). Facing South.
- FOV South covers Cone downwards.
- F is at (4, 8).
- Vector from (8,6) to (4,8) is (-4, 2). South-West.
- Angle: atan2(2, -4) relative to South (0, 1)?
- South vector (0, 1). Target (-4, 2).
- Angle is roughly 63 deg West of South.
- FOV is 45 deg.
- F is **Outside** FOV (too far West).
- **F is UNEXPLORED.**
- Blue Door + (Row 9, Col 6).
- Vector from (8,6) to (6,9) is (-2, 3).
- Angle relative to South (0, 1).
- atan(2/3) approx 33 deg West of South.
- Inside FOV. (Agent saw Blue Door).

Room 2 Candidates:
- Agent went to Books (approx Row 4, Col 9/10?).
- Looked South. Covered D (Row 6, Col 10?). Yes.
- Looked West. Covered back to door.
- Never looked North in Room 2.
- **G, B, I are UNEXPLORED.**
- **C, E**?
- C is Row 4, Col 9. E is Row 4, Col 11.
- "Books" were found. Agent jumped to Books.
- If Books is at E, Agent at E looked South.
- Did Agent see C?
- Agent at Yellow Door looked East. Saw Books (mid dist).
- Yellow Door (8,6). Books (say 11, 4).
- Vector (3, -2). South-East?
- Agent facing East. (3, -2) is 33 deg South of East. Inside FOV.
- C is at (9, 4). Vector (1, -2). 63 deg South of East. Outside FOV.
- Wait, if C is outside, is it unexplored?
- Agent jumped to Books. From Books (11,4) looked West?
- Vector to C (9,4) is (-2, 0). West. Inside West FOV.
- **C is OBSERVED.**
- **E is OBSERVED** (Agent likely at or near E).

Summary of Unexplored:
Room 1: H, J, F. (South-West / South-Central area).
Room 2: G, B, I. (North area).

Check F again.
Pos (8,6) facing South.
F (4,8).
Rel pos: x=-4, y=+2 (Down).
Angle: atan(4/2) = 63 deg. > 45.
So F is not seen from Yellow Door facing South.
Was F seen from Start (4,6)?
Look North (Up). No.
Look East (Right). No.
So F is Unexplored.

Check H, J again.
(2, 7) and (3, 7).
From Start (4,6).
North: No.
East: No.
From Yellow Door (8,6) facing South.
Vector (-6, 1) / (-5, 1).
Way out of South FOV.
Unexplored.

Check A.
(6, 7).
From Start (4,6) looking East?
Vector (2, 1). Angle 26 deg. Seen.
From Yellow Door (8,6) looking South?
Vector (-2, 1). Angle 26 deg. Seen.
So A is Observed.

Final Unexplored List:
B, F, G, H, I, J.

Wait, look at map again for B, G, I.
Row 1: .GB...
Row 2: ..I...
All in North of Room 2.
Agent never looked North in Room 2.
So B, G, I are Unexplored.

Room 1:
H, J (Row 7, Left).
F (Row 8, Mid-Left).
Agent never looked West or South-West in Room 1.
So H, J, F are Unexplored.

Candidates to select: B, F, G, H, I, J.

Double check K.
Row 3, Col 2.
Start (4,6). Look North (Up).
Vector (-2, -3). Angle 33 deg. Inside FOV.
K is Observed.

Double check A.
Row 7, Col 6.
Start (4,6). Look East.
Vector (2, 1). Angle 26 deg. Inside FOV.
A is Observed.

Double check C.
Row 4, Col 9.
From Books (say 11,4) looking West.
Vector (-2, 0). Seen.
C is Observed.

Double check D.
Row 6, Col 10.
From Books (11,4) looking South.
Vector (-1, 2). Angle 26 deg. Seen.
D is Observed.

Double check E.
Row 4, Col 11.
Likely the location of Books or near it. Seen.

Double check L.
Row 5, Col 6.
Start (4,6) Look East.
Vector (2, -1). Angle 26 deg. Seen.
L is Observed.

Result: B, F, G, H, I, J.

Is there any ambiguity about Start Position?
"treat your initial position as the origin (0, 0)".
If (0,0) is origin, and North is +y.
Saw Yellow Door (East).
Saw Blue Door (Right -> South).
This relative geometry holds.
The absolute map coordinates in the Fog Probe might be shifted.
The key is the relative positions.
K is North-West of Start. Start looked North. Seen.
H, J are South-West of Start. Start looked North then East. Not Seen.
F is South of Start. Start looked North then East. Not Seen.
A is South-East of Start. Seen (Look East).
L is North-East of Start. Seen (Look East).

So F, H, J are Unexplored in Room 1.
B, G, I are Unexplored in Room 2.

Final check on F.
Agent at Yellow Door (East of Start) looking South.
F is South-West of Yellow Door.
If F is far enough West, it's outside the South cone.
F is at x=4. Yellow Door is at x=8.
Dy = 2. Dx = 4. Angle 63 deg. Outside.
Correct.

Final Answer seems to be B, F, G, H, I, J.

FINAL ANSWER:
{
"unexplored": ["B", "F", "G", "H", "I", "J"]
}

THINK:
The agent started at (0,0) (let's assume relative to the map visualization, the map coordinates provided in the text description differ from the fog probe map which uses a grid visualization).
Let's analyze the Fog Probe Map.
The map shows walls ('#'), doors ('+'), and the agent's position ('...

################
#########.GB...#
#########..I...#
##K.....#......#
##......#C.E...#
##....L.#......#
##......*.D....#
##HJ..A.########
##..F...########
######+#########
#......#########
#......#########
#......#########
#......#########
#......#########
#......#########
################

You jumped to yellow door. You rotated counterclockwise 90°. You observe:
• blue door: front-right, mid distance, on front wall.
You have a maximum of 14 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to yellow door. You rotated counterclockwise 90°. You observe:
• blue door: front-right, mid distance, on front wall.
You have a maximum of 14 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at the "yellow door" facing South. The "blue door" is visible to the front-right. The goal is to explore the room connected by the "blue door" (Room 3).
1. Jump to "blue door". This places the agent in the doorway of Room 3.
2. The agent's orientation remains South.
3. Observe from the doorway to see the contents of Room 3.

The agent is at the "yellow door" facing South. The "blue door" is visible to the front-right. The goal is to explore the room connected by the "blue door" (Room 3).
1. Jump to "blue door". This places the agent in the doorway of Room 3.
2. The agent's orientation remains South.
3. Observe from t...

THINK:
I need to reconstruct the global map based on the sequence of observations and movements.
Initial State: Agent at (0,0), facing North (+y).
1. **Observe**: Nothing.
2. **Rotate(90)**: Facing East (+x). Agent at (0,0).
3. **Observe**:
* `yellow door`: front-slight-right, slightly far, on front wall. Front is East. Front-slight-right suggests it's mainly East but slightly South. Distance ~5. Let's estimate position. "On front wall" usually implies it aligns with the grid in front. Let's place it at (5, -1) or (5,0). Wait, "front-slight-right" means angle > 0 (right is +). East is 0. Slight right is towards South. So y is negative. Let's guess (5, -2).
* `blue door`: front-right, slightly far, on right wall. Front is East. Right is South. "On right wall" means it's on the South wall. Distance ~5. Direction is roughly South-East. Position maybe (2, -5) or (3, -5).
* `shoes`: front-slight-right, slightly far. Near yellow door. Maybe (4, -2).
* `rubberduck`: front-right, mid distance. South-East. Maybe (3, -3).
* `alarmclock`: front-left, mid distance. North-East. Maybe (3, 2).
* Relations: shoes near yellow door (makes sense). rubberduck near alarmclock (weird, one is SE, one is NE? "front-left" vs "front-right"). Wait, "rubberduck: front-right", "alarmclock: front-left". "rubberduck is east, near to alarmclock". This implies they are close. Let's re-evaluate.
* Let's refine coordinates based on steps.
* Agent at (0,0).
* JumpTo(yellow door). Agent now at yellow door position. Let's call it $P_{yd}$.
* Observe from $P_{yd}$ facing East.
* `laptop`: front-left (NE), slightly far.
* `airplane`: front-left (NE), slightly far.
* `backpack`: front-slight-left (E/NE), slightly far.
* `books`: front (E), mid distance (~3-4).
* $P_{books}$ is roughly $P_{yd} + (4, 0) = (9, -2)$?
* JumpTo(books). Agent at $P_{books}$.
* Rotate(90) -> Facing South. Observe: Nothing.
* Rotate(90) -> Facing West. Observe: `yellow door` front, mid distance. Distance to yellow door is ~3-4. This confirms books is directly East of yellow door.
* JumpTo(yellow door). Back at $P_{yd}$.
* Rotate(-90) -> Facing South.
* Observe: `blue door` front-right, mid distance (~3-4). Front is South. Right is West. So blue door is South-West of yellow door?
* Let's check initial observation again. At (0,0) facing East: `yellow door` (front-slight-right ~ ESE), `blue door` (front-right ~ SE/SSE).
* From $P_{yd}$ facing South: `blue door` is front-right (SW).
* If $P_{yd} = (5, -2)$. South is -y. Right is -x. So SW is correct.
* $P_{bd}$ should be roughly $(5-2, -2-3) = (3, -5)$?
* Distance from (0,0) to (3,-5) is $\sqrt{9+25} \approx 5.8$ (slightly far). Consistent.
* Angle from (0,0) facing East to (3,-5): Vector (3, -5). East is (1,0). Angle is atan2(-5, 3) $\approx -59^\circ$. This is "front-right" (22.5 to 45) or beyond?
* Wait, bins: "front-right" is (22.5, 45]. -59 is > 45. That would be "right".
* Let's adjust. Maybe $P_{yd} = (4, 0)$?
* At (0,0) facing East. $P_{yd}=(4,0)$ is "front". But observed "front-slight-right". So maybe $(4, -1)$. Angle $\approx -14^\circ$. "front-slight-right" is (0, 22.5]. OK.
* $P_{bd}$: From $P_{yd}(4,-1)$ facing South, it's "front-right" (SW). Vector $P_{bd} - P_{yd} = (-dx, -dy)$.
* From (0,0) facing East, $P_{bd}$ is "front-right" (SE). Vector $(x, y)$ with $x>0, y<0$. Angle in (22.5, 45).
* Let's try $P_{bd} = (3, -3)$. From (0,0): $\sqrt{18} \approx 4.2$. Angle $-45$. Borderline front-right/right.
* From $P_{yd}(4,-1)$ facing South: $P_{bd}(3,-3) - (4,-1) = (-1, -2)$. Relative to South (0,-1): Forward is -y. Right is -x. (-1, -2) is 1 unit Right, 2 units Forward. Angle atan2(1, 2) $\approx 26^\circ$. "front-right" is (22.5, 45]. Perfect.
* So: $P_{yd} \approx (4, -1)$. $P_{bd} \approx (3, -3)$.
* Wait, distance "mid distance" is (2,4]. $\sqrt{5} \approx 2.2$. Matches.
* JumpTo(blue door). Agent at $P_{bd} \approx (3, -3)$. Facing South.
* Observe:
* `shoppingcart`: front (South), slightly far (4-8). $P_{cart} \approx (3, -3) + (0, -5) = (3, -8)$.
* `red chair`: front-right (SW), mid distance (2-4). $P_{chair} \approx (3, -3) + (-2, -3) = (1, -6)$?
* Facing South. Front is -y. Right is -x. Front-right is -x, -y.
* Let's check constraints.

Refining Coordinates:
1. Agent (0,0).
2. Yellow Door: $(4, -1)$.
3. Blue Door: $(3, -3)$.
4. Shoes: Near Yellow Door. Initial Obs (0,0)->E: "front-slight-right". Pos roughly $(3, -1)$? Distance $\sqrt{10} \approx 3.1$ (mid/sl-far).
5. Rubberduck: Initial Obs (0,0)->E: "front-right". Pos roughly $(3, -2)$?
6. Alarmclock: Initial Obs (0,0)->E: "front-left". Pos roughly $(3, 1)$?
7. Room 2 (East of Yellow Door):
* Books: From $P_{yd}(4,-1)$ facing East. "front", mid-dist (2-4). Say distance 3. $P_{books} = (7, -1)$.
* Laptop: From $P_{yd}$ facing East. "front-left" (NE).
* Airplane: "front-left".
* Backpack: "front-slight-left".
8. Room 3 (South of Blue Door):
* From $P_{bd}(3,-3)$ facing South.
* Shoppingcart: "front" (S). Slightly far (4-8). Say dist 5. $P_{cart} = (3, -8)$.
* Red chair: "front-right" (SW). Mid dist (2-4). Say dist 3. Angle ~30-40 deg. $x \approx 3 - 3\sin(30) = 1.5$, $y \approx -3 - 3\cos(30) = -5.6$. Integer grid: maybe $(2, -6)$?

Let's verify "on right wall" for Blue Door from (0,0) facing East. Right wall is South wall. $(3, -3)$ fits nicely as a door on a south wall of a room spanning roughly x=0..5, y=0..-3.
Let's verify "on front wall" for Yellow Door from (0,0) facing East. Front wall is East wall. $(4, -1)$ fits as a door on east wall.

Objects:
- Shoes: $(3, -1)$
- Rubberduck: $(3, -2)$
- Alarmclock: $(3, 1)$
- Yellow Door: $(4, -1)$
- Blue Door: $(3, -3)$
- Books: $(7, -1)$
- Laptop: $(6, 1)$ (From YD(4,-1) facing E, NE is +x,+y. dx=2, dy=2? dist 2.8. Slightly far is >4. Maybe dx=4, dy=2? (8, 1). Distance 4.5.)
- Airplane: $(8, 2)$
- Backpack: $(8, 0)$
- Shoppingcart: $(3, -8)$
- Red chair: $(1, -6)$

Let's do integer approximation.
Agent at Blue Door $(3, -3)$, Facing South.

Final JSON Construction:
Agent: [3, -3], facing "south"
Shoes: [3, -1], facing "south" (observed facing "backward" from East view -> West? No, "facing backward" means the object's front is opposite to agent's view. Agent looked East. Object faces West. "South" in map? The prompt says "facing backward" relative to agent. Agent facing East. Object faces West. But shoes don't have intrinsic front usually. Oh, "shoes... facing backward". Let's ignore facing for non-oriented objects unless specified? "facing" is in schema. OK. "facing backward" relative to agent's East view = West. )
Actually, let's look at the "facing" property in observations:
- shoes: facing backward (relative to agent facing East) -> Faces West.
- rubberduck: facing left (relative to agent facing East) -> Faces North.
- alarmclock: facing backward (relative to agent facing East) -> Faces West.
- laptop: facing forward (relative to agent facing East) -> Faces East.
- airplane: facing right (relative to agent facing East) -> Faces South.
- backpack: facing left (relative to agent facing East) -> Faces North.
- shoppingcart: facing forward (relative to agent facing South) -> Faces South.
- red chair: facing forward (relative to agent facing South) -> Faces South.

Wait, "red chair ... facing forward". Agent facing South. So chair faces South.

Coordinates Recap:
Agent: [3, -3], facing South.
Yellow Door: [4, -1]
Blue Door: [3, -3]
Shoes: [3, -1]
Rubberduck: [3, -2]
Alarmclock: [3, 1]
Books: [7, -1]
Laptop: [8, 1]
Airplane: [8, 2]
Backpack: [8, 0]
Shoppingcart: [3, -8]
Red Chair: [1, -5]

Let's double check spatial relations provided in text to refine relative positions.
Obs 1 (facing E):
- shoes north of rubberduck. (3,-1) is north of (3,-2). OK.
- shoes south of yellow door? (3,-1) vs (4,-1). No, that's West.
Text says: "shoes is south, near to yellow door".
If Yellow Door is at (4, 0) and Shoes at (4, -1)?
Then Blue Door at (3, -3).
Obs 1: Yellow Door front-slight-right (4,0) from (0,0) facing E is "front". Not slight right.
If Yellow Door is (4, -1) and Shoes at (4, -2)?
Shoes south of YD. Correct.
Shoes north of rubberduck. Rubberduck at (4, -3)?
Rubberduck "front-right" from (0,0)E. (4,-3) angle ~ -37. OK.
Blue Door "front-right". (3, -3). Angle -45. OK.
Alarmclock "front-left". (3, 1). Angle ~18. OK.
Rubberduck East of Alarmclock? (4,-3) vs (3,1). Yes 4 > 3. OK.

So let's shift YD and Room 2 objects.
YD: (4, -1)
Shoes: (4, -2)
Rubberduck: (4, -3)
Alarmclock: (3, 1)
BD: (3, -3)

Room 2 (from YD (4,-1)):
Books: "front" (E). (7, -1).
Laptop: "front-left" (NE). "South, near backpack". "West, near books".
If Books is (7, -1). Laptop West -> (6, -1)? No, "front-left".
Let's look at "Assume your current facing direction is called north". Agent facing East.
"Laptop is south, near to backpack". (Relative: Laptop is Right of Backpack).
"Laptop is west, near to books". (Relative: Laptop is Behind Books).
Real coordinates (North is +y):
Agent facing East.
"South" relative to agent = Right (Global South).
"West" relative to agent = Behind (Global West).
So: Laptop is Global South of Backpack. Laptop is Global West of Books.
Books at (7, -1). Laptop West -> (6, -1)?
Laptop South of Backpack -> Backpack at (6, 0)?
Check visual: Agent at (4,-1) facing E.
Books (7,-1): Front. OK.
Backpack (6,0): Front-Left. OK.
Laptop (6,-1): Front. Not Front-Left.
Maybe Laptop is (6, 0.5)? No integers.
Maybe Books is (8, -1). Laptop (7, -1) is West.
Backpack (7, 0). Laptop South of Backpack.
Visual:
Books (8, -1) -> Front, mid dist (4).
Backpack (7, 0) -> Front-Left (dx=3, dy=1). Angle 18. "Front-slight-left". OK.
Laptop (7, -1) -> Front (dx=3, dy=0).
But text says "Laptop: front-left".
So Laptop must have dy > -1.
Let's reconsider the "Assume..." block.
"Assume your current facing direction is called north".
This defines a local frame where Local North = Global East.
"Laptop is south [Local South], near to backpack". Local South = Global South.
"Laptop is west [Local West], near to books". Local West = Global West.
So Laptop is Global South of Backpack. Laptop is Global West of Books.
This matches my derivation.
Constraint: Laptop must be Front-Left (Global NE) from (4,-1). So $y_{laptop} > -1$.
But Laptop is South of Backpack. So $y_{laptop} < y_{backpack}$.
So $-1 < y_{laptop} < y_{backpack}$.
Let's try $y_{laptop} = 0, y_{backpack} = 1$.
$x_{laptop} < x_{books}$.
Let $x_{laptop} = 6, x_{books} = 7$.
Check:
Agent (4, -1).
Laptop (6, 0): dx=2, dy=1. Angle 26. Front-right? No, Front-Left is +y relative to front. Yes. Front is +x. Left is +y. Angle +26. "Front-right" is (22.5, 45] in egocentric?
Ego Front is 0. Front-Left is [-45, 0) or (0, 45]?
Prompt: "[-45°,-22.5°)→front-left, [-22.5°,0°)→front-slight-left, ... (22.5°,45°]→front-right".
Wait, positive is clockwise.
Agent facing East.
Object at (6, 0) is to the "Left" (North).
Vector (2, 1). Angle wrt East (1,0) is +26 degrees CCW.
CCW is negative degrees in this prompt? "Positive = clockwise".
So Angle is -26.
-26 falls in [-45, -22.5). "front-left". Correct.
Object Backpack (6, 1): dx=2, dy=2. Angle -45. Borderline. Maybe (7, 1)?
Object Books (7, -1): dx=3, dy=0. Angle 0. "front". Correct.
So: Laptop (6, 0), Backpack (6, 1), Books (7, -1).
Airplane? "front-left". "Airplane is west, near to backpack".
Local West = Global West. Airplane is Global West of Backpack.
Backpack (6, 1). Airplane (5, 1)?
Check visual: Agent (4, -1). Airplane (5, 1). dx=1, dy=2. Angle atan2(2,1) = 63 deg CCW -> -63. "Beyond FOV"?
Limit is 45.
Maybe scale up.
Books (8, -1). Laptop (7, 0). Backpack (7, 1). Airplane (6, 1).
Agent (4, -1). Airplane (6, 1). dx=2, dy=2. Angle -45. "front-left". OK.
Laptop (7, 0). dx=3, dy=1. Angle -18. "front-slight-left".
Obs says "Laptop: front-left". Needs angle < -22.5.
Maybe Laptop (6, 1), Backpack (6, 2), Airplane (5, 2)?
Let's stick to valid grid positions.
Let's assume:
Books: (8, -1)
Laptop: (7, 1)
Backpack: (7, 2)
Airplane: (6, 2)
Agent (4, -1).
Laptop (7, 1) -> dx=3, dy=2. Angle -33. Front-left. OK.
Backpack (7, 2) -> dx=3, dy=3. Angle -45. Front-left. (Obs says front-slight-left? No, Obs says "backpack: front-slight-left").
Contradiction.
Let's ignore the exact "front-left" vs "front-slight-left" fine distinction if it conflicts with spatial relations. The spatial relations "South of", "West of" are usually more robust topological clues.
Relations:
L is S of Bp.
L is W of Bk.
A is W of Bp.
Grid:
A Bp
. L Bk
(North is Up)
Map to Global:
Bp is North of L. Bk is East of L. A is West of Bp.
Y coords: Bp, A > L.
X coords: A < Bp. L < Bk.
And L is in FOV of (4, -1) facing East. Y_L >= -1.
If Y_L = 0. Y_Bp = 1.
X_L = 7. X_Bk = 8. X_Bp = 7. X_A = 6.
Positions:
L(7,0), Bk(8,0), Bp(7,1), A(6,1).
Check view from (4, -1) East.
L(7,0): dx=3, dy=1. Angle -18. "front-slight-left". Obs: "front-left". (Mismatch).
Bp(7,1): dx=3, dy=2. Angle -33. "front-left". Obs: "front-slight-left". (Mismatch).
Maybe my angle sign convention is wrong?
"0° is front. +: clockwise".
Left is Counter-Clockwise (Negative).
Right is Clockwise (Positive).
If I face East. North is Left (-). South is Right (+).
L(7,0) is North (Left). Angle -18.
"[-22.5, 0) -> front-slight-left".
"[-45, -22.5) -> front-left".
L(7,0) is front-slight-left. Obs says front-left.
I need L to be more Left (more North).
Try L(6, 1). dx=2, dy=2. Angle -45. front-left. OK.
Then Bp must be North of L -> (6, 2).
Bk East of L -> (7, 1).
A West of Bp -> (5, 2).
Check Bp(6, 2) from (4, -1). dx=2, dy=3. Angle -56. Beyond FOV?
FOV is 90 (-45 to 45). Yes, 56 is outside.
So this config is impossible.

Let's swap the "front-left" / "front-slight-left" labels. Maybe I transcribed them wrong?
"laptop: front-left"
"backpack: front-slight-left"
This implies Laptop is MORE left (more North) than Backpack.
But "Laptop is south of Backpack". Laptop is LESS North than Backpack.
This is a direct contradiction between the Egocentric labels and the Allocentric relations provided in the prompt "Assume...".
Usually the "Assume..." text describes local relations between objects.
"Laptop is south, near to backpack". (Laptop has smaller Y than Backpack).
"Laptop (angle L) is front-left (more negative). Backpack (angle B) is front-slight-left (less negative)".
Angle L < Angle B. (e.g. -40 < -10).
So Laptop is more CCW.
Position L(xL, yL). Position B(xB, yB).
Agent at origin.
atan2(yL, xL) > atan2(yB, xB)? No, atan2 returns CCW from x axis?
Standard math: atan2(1, 1) = 45 deg.
My angles: Left is Negative.
So L is more Left -> Angle L is more negative (e.g. -40).
B is less Left -> Angle B is less negative (e.g. -10).
So L has larger Y/X ratio than B?
yL/xL > yB/xB?
If L is South of B (yL < yB).
Then we need xL such that yL/xL > yB/xB with yL < yB.
This requires xL much smaller than xB.
L is "West" of something? "Laptop is west, near to books".
"Airplane is west, near to backpack".
L is South of B.
If L(5, 1) and B(8, 2).
yL=1, xL=5. Ratio 0.2. Angle ~11 deg (front-slight-left).
yB=2, xB=8. Ratio 0.25. Angle ~14 deg (front-slight-left).
This doesn't fit the "front-left" vs "front-slight-left" distinction well.
Let's try L(5, 2) and B(8, 2)? L South of B? No.

Let's prioritize the Allocentric Relations ("L is South of B").
Map:
B (North)
L (South)
Positions: B(7, 1), L(7, 0).
View from (4, -1).
L: (3, 1). Angle -18. "front-slight-left".
B: (3, 2). Angle -33. "front-left".
My obs: L="front-left", B="front-slight-left".
This is the opposite.
Maybe "Laptop is south, near to backpack" means Global South?
Yes, "south" usually means global south.
Maybe the labels in the prompt are noisy or I am misinterpreting "front-left".
Let's stick to the coordinates derived from the "Assume" block as it's more explicit about relative topology.
Topology:
Bp
A L Bk
(With A West of Bp? No, A West of Bp. L South of Bp. L West of Bk.)
Wait, "Airplane is west, near to backpack".
So A is West of Bp.
Bp
A
And L is South of Bp.
And L is West of Bk.
Bp
A L Bk ?? No, A is West of Bp, not L.
Row 1 (North): A, Bp
Row 2 (South): L, Bk
Cols: A < Bp. L < Bk.
And L is South of Bp. (So L is under Bp).
So:
A Bp
L Bk
Coordinates:
A(6, 1), Bp(7, 1)
L(7, 0), Bk(8, 0)
Check View from (4, -1):
L(7,0): dx=3, dy=1. Angle -18 (front-slight-left). Obs: front-left.
Bk(8,0): dx=4, dy=1. Angle -14 (front-slight-left). Obs: front.
Bp(7,1): dx=3, dy=2. Angle -33 (front-left). Obs: front-slight-left.
A(6,1): dx=2, dy=2. Angle -45 (front-left). Obs: front-left.

There is a systematic error in my angle interpretation vs observations.
Obs says L is "Left" (more angle) and Bp is "Slight Left" (less angle).
Model says L is "Slight Left" and Bp is "Left".
This happens if L is actually North of Bp?
But text says "Laptop is south... of backpack".
Could "south" mean "ego south" (right)?
"Assume your current facing direction is called north".
Ego North = Agent Facing (East).
Ego South = Right (West).
"Laptop is ego-south (West) of Backpack".
"Laptop is ego-west (Left/North) of Books".
If Laptop is West(Global) of Backpack.
And Laptop is North(Global) of Books.
Then L is Left(Ego) of Bp (consistent with "front-left" vs "slight-left").
And L is Left(Ego) of Bk.
This contradicts "Laptop is west [Global?], near to books".
Let's assume the "Assume..." block uses Global Directions relative to the temporary North frame.
Temporary North = Agent Facing (East).
"Laptop is south (Right -> Global South) of Backpack".
This is what I used.

Maybe the agent moved?
No, "Observe action only reports from your current position".

Let's trust the "Assume" block for topology.
A(6, 1), Bp(7, 1), L(7, 0), Bk(8, 0).
This fits "A West of Bp", "L South of Bp", "L West of Bk".
We will use these coordinates.

Room 3:
Agent at Blue Door (3, -3) facing South.
"shoppingcart is south... of nothing".
"shoppingcart: front (S), slightly far". (3, -8).
"red chair: front-right (SW), mid dist". (1, -5).
"red chair is facing forward" (South).
"shoppingcart is facing forward" (South).

Final Object List:
Shoes: [4, -2], facing "west" (backward from East view)
Rubberduck: [4, -3], facing "north" (left from East view)
Alarmclock: [3, 1], facing "west" (backward from East view)
Yellow Door: [4, -1]
Blue Door: [3, -3]
Books: [8, 0], facing "west" (agent facing E saw books "front", dist 3-4? from 4,-1. say (8,-1). Wait, earlier I said (7,-1) or (8,0). Let's use (8,-1). Bk East of L(7,-1). L South of Bp(7,0). A West of Bp(6,0).
Let's re-verify A(6,0) from (4,-1). dx=2, dy=1. Angle -26. Front-left. Matches Obs.
Bp(7,0) from (4,-1). dx=3, dy=1. Angle -18. Front-slight-left. Matches Obs!
L(7,-1) from (4,-1). dx=3, dy=0. Angle 0. Front. Matches Obs? Obs says "Laptop: front-left".
This is the problem. Laptop cannot be at y=-1 (Front). It must be y > -1.
If L(7,0). Bp(7,1). A(6,1). Bk(8,0).
L(7,0) from (4,-1) -> Angle -18. Front-slight-left. Obs: Front-left.
Maybe L(6,0)? dx=2, dy=1. Angle -26. Front-left. Match!
Then Bp North of L -> Bp(6,1)?
Bp(6,1) from (4,-1) -> dx=2, dy=2. Angle -45. Front-left. Obs: Front-slight-left. (Mismatch).
Let's settle on:
L: [6, 0] (front-left)
Bp: [7, 1] (front-slight-left, further away)
A: [6, 1] (front-left, near Bp? No A is West of Bp. 6 < 7. OK.)
Bk: [7, 0] (front, near L. L is West of Bk. 6 < 7. OK.)
Check views:
L(6,0) from (4,-1): dx=2, dy=1. Ang -26. FL. OK.
A(6,1) from (4,-1): dx=2, dy=2. Ang -45. FL. OK.
Bp(7,1) from (4,-1): dx=3, dy=2. Ang -33. FL. Obs: FSL. Close enough.
Bk(7,0) from (4,-1): dx=3, dy=1. Ang -18. FSL. Obs: Front. Close enough.
This seems the best fit.

Final Coordinates:
Agent: [3, -3], facing "south"
Shoes: [4, -2], facing "west"
Rubberduck: [4, -3], facing "north"
Alarmclock: [3, 1], facing "west"
Yellow Door: [4, -1]
Blue Door: [3, -3]
Laptop: [6, 0], facing "east"
Airplane: [6, 1], facing "south"
Backpack: [7, 1], facing "north"
Books: [7, 0]
Shoppingcart: [3, -7], facing "south" (dist ~4)
Red chair: [1, -5], facing "south"

Facing directions:
- shoes: backward from East -> West
- rubberduck: left from East -> North
- alarmclock: backward from East -> West
- laptop: forward from East -> East
- airplane: right from East -> South
- backpack: left from East -> North
- shoppingcart: forward from South -> South
- red chair: forward from South -> South

FINAL ANSWER:
```json
{
"agent": {"position": [3, -3], "facing": "south"},
"shoes": {"position": [4, -2], "facing": "west"},
"rubberduck": {"position": [4, -3], "facing": "north"},
"alarmclock": {"position": [3, 1], "facing": "west"},
"yellow door": {"position": [4, -1]},
"blue door": {"position": [3, -3]},
"laptop": {"position": [6, 0], "facing": "east"},
"airplane": {"position": [6, 1], "facing": "south"},
"backpack": {"position": [7, 1], "facing": "north"},
"books": {"position": [7, 0]},
"shoppingcart": {"position": [3, -7], "facing": "south"},
"red chair": {"position": [1, -5], "facing": "south"}
}
```

THINK:
I need to reconstruct the global map based on the sequence of observations and movements.
Initial State: Agent at (0,0), facing North (+y).
1. **Observe**: Nothing.
2. **Rotate(90)**: Facing East (+x). Agent at (0,0).
3. **Observe**:
* `yellow door`: front-slight-right, slightly far,...

{
  "agent": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      4,
      -2
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      4,
      -3
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      3,
      1
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      4,
      -1
    ]
  },
  "blue door": {
    "position": [
      3,
      -3
    ]
  },
  "laptop": {
    "position": [
      6,
      0
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      6,
      1
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      7,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      7,
      0
    ]
  },
  "shoppingcart": {
    "position": [
      3,
      -7
    ],
    "facing": "south"
  },
  "red chair": {
    "position": [
      1,
      -5
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -4
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -4
    ],
    "facing": "south"
  }
}

THINK: The agent is at the "blue door", facing South.
The observation reports:
- shoppingcart: front, slightly far. "Front" means +y relative to agent. "Slightly far" is distance bin (4, 8]. Let's estimate y=5. x=0. Relative position [0, 5]. "facing forward": since agent faces South, "forward" (ego) means South. But usually "facing forward" for an object means it faces the agent or the same direction? The prompt says "forward/backward/right/left (ego) or north/east/south/west (allo)". "When agent faces north: forward = north". Here agent faces South. So "forward" means South. The object "facing forward" likely means its intrinsic front is aligned with the agent's facing direction (South). Let's map "forward" to +y in the local frame.
- red chair: front-right, mid distance. "Front-right" means angle (22.5, 45]. "Mid distance" is (2, 4]. Let's say distance 3. Angle ~30 deg. x = 3*sin(30) = 1.5, y = 3*cos(30) = 2.6. Round to integers: [1, 3] or [2, 2]. Let's pick [2, 3]. "facing forward" -> +y.

Wait, looking at previous examples or instructions? "Relationship: bearing in degrees... Orientation: -forward/backward/right/left (ego)... When agent faces north: forward = north".
Here agent is facing South.
Object "shoppingcart" is "facing forward".
Local frame: +y is agent's forward (South).
So object faces +y (South).
Object "red chair" is "facing forward".
Faces +y (South).

Let's refine coordinates.
shoppingcart: front (0 deg), slightly far (4-8m). Let's say [0, 5].
red chair: front-right (22.5-45 deg), mid distance (2-4m). Let's say [2, 3].

Wait, "blue door" is where the agent is. The observation is FROM the blue door looking into the room.
The JSON must represent the *current* observation relative to the agent.
Origin: agent (at blue door).
Axes: +y is forward (South in global), +x is right (West in global).

Objects:
1. "shoppingcart": front, slightly far. -> x=0, y=~5. Facing: forward -> +y.
2. "red chair": front-right, mid distance. -> x>0, y>0. Say x=2, y=3. Facing: forward -> +y.

JSON structure:
{
"origin": "agent",
"objects": {
"shoppingcart": {"position": [0, 5], "facing": "+y"},
"red chair": {"position": [2, 3], "facing": "+y"}
}
}
Note: Coordinates are integers. "slightly far" is >4. "mid distance" is >2.

Let's check the previous turn's specific phrasing.
"facing forward" in observation usually describes the object's orientation relative to the agent's view.
If I face South, and object faces "forward", it faces South. In local frame (+y = South), it faces +y.

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"shoppingcart": {"position": [0, 5], "facing": "+y"},
"red chair": {"position": [2, 3], "facing": "+y"}
}
}

THINK: The agent is at the "blue door", facing South.
The observation reports:
- shoppingcart: front, slightly far. "Front" means +y relative to agent. "Slightly far" is distance bin (4, 8]. Let's estimate y=5. x=0. Relative position [0, 5]. "facing forward": since agent faces South, "forward" (ego)...

{
  "origin": "agent",
  "objects": {
    "shoppingcart": {
      "position": [
        0,
        5
      ],
      "facing": "+y"
    },
    "red chair": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    }
  }
}

{
  "red chair": {
    "position": [
      2,
      3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      0,
      5
    ],
    "facing": "south"
  }
}

{
  "origin": "agent",
  "objects": {
    "shoppingcart": {
      "position": [
        0,
        5
      ],
      "facing": "+y"
    },
    "red chair": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    }
  }
}

{
  "red chair": {
    "position": [
      2,
      3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      0,
      5
    ],
    "facing": "south"
  }
}

THINK:
1. **Analyze the current state:**
* Agent is at the `blue door` (marked as `*` on the map).
* Agent is facing South (down on the map).
* Agent just observed Room 3 (South of the blue door).
* Objects observed in Room 3: `shoppingcart` (front/South, slightly far), `red chair` (front-right/South-West, mid distance).

2. **Analyze the map layout and history:**
* **Room 1 (Start Room):**
* Initial pos (0,0) was origin. Agent faced North, saw nothing.
* Rotated East, saw `shoes`, `rubberduck`, `alarmclock`, `yellow door` (East), `blue door` (South relative to initial, but description said "front-right" when facing East... wait, let's re-read).
* Re-reading Step 2: At (0,0) facing East. `yellow door` front-slight-right (East-ish). `blue door` front-right (South-East-ish).
* Re-reading Step 6 (current): Agent jumped to `yellow door`, rotated to face South. `blue door` was front-right. Agent jumped to `blue door`. Map shows agent `*` on a horizontal wall separating a northern area and a southern area.
* The map shows a room to the North-West of `*` (Room 1), a room to the North-East of `*` (Room 2, accessed via `yellow door`), and a room to the South of `*` (Room 3).
* Wait, let's trace the path on the ASCII map.
* The ASCII map shows:
* Top-left area: Seems like Room 1?
* Top-right area: Seems like Room 2? (Points A, C, D, F, Q, R are there). The `+` at `(row 7 from bottom, col 9)` looks like the `yellow door` connecting the left and right upper rooms.
* Agent `*` is at `(row 10 from top approx)`. Let's look at coordinates. (0,0) is bottom-left.
* The `+` between the left room and right room is at roughly `x=8, y=7` (counting visually).
* The agent `*` is at a door connecting the top-left room and a bottom room. Wait, let's look at the structure.
* Structure:
* Upper Left Room (Room 1): Contains G, H, P, L, K, O.
* Upper Right Room (Room 2): Contains F, Q, D, A, C, R. Connected to Room 1 by a door `+` (let's call it Door 1).
* Lower Room (Room 3): Contains I, J, E, M, N, B. Connected to Room 1 by a door `*` (Agent is here).
* **Verify Room Identity:**
* Agent started in Room 1.
* Found `yellow door` (to Room 2). Jumped there. Saw `laptop`, `airplane`, `backpack`, `books`.
* Jumped to `books` (Room 2).
* Jumped back to `yellow door`.
* Jumped to `blue door`.
* Current observation: `shoppingcart`, `red chair` in Room 3 (South).
* **Map Interpretation:**
* The wall separating Room 1 and Room 2 is vertical (x=8ish). The door is `+` at y=7ish.
* The wall separating Room 1 and Room 3 is horizontal (y=6ish). The door is `*` (where the agent is).
* Room 2 (Top Right) has been observed from the `yellow door` and from `books`.
* Observed from `yellow door` (looking East): `laptop`, `airplane`, `backpack`, `books`.
* Observed from `books` (looking South): Saw nothing.
* This implies the northern part of Room 2 is observed. The southern part (A, C) might be unobserved or "beyond FOV" in previous steps? Let's check.
* From `yellow door` (looking East/into Room 2): FOV covers East.
* From `books` (looking South): FOV covers South.
* Points A, C are in the "middle" or "south" of Room 2. `books` was "front, mid distance" from `yellow door`. `books` is likely near the East wall or center. From `books`, looking South saw nothing. This suggests the area South of `books` is empty or observed as empty.
* Point F, Q, D are in the North of Room 2.
* Point A, C are in the South of Room 2.
* From `yellow door` looking East: `books` is front. Objects `laptop`, `airplane`, `backpack` were front-left (North).
* So the North part of Room 2 (F, Q, D) contains objects. The South part (A, C) was scanned when looking South from `books`. Wait, "You rotated clockwise 90°. You observe: No objects in field of view." This means the area South of `books` is empty of *objects*, but the space itself has been "observed". The question asks for "unexplored/unobserved regions".
* If I observed a region and saw "No objects", is it unobserved? No, it's observed to be empty.
* However, did the FOV cover points A and C?
* `books` position: From `yellow door` (assume (0,0) of Room 2 is door), books is East. Let's say (4,0).
* Looking South from (4,0) covers the South-East quadrant relative to `books`.
* Points A and C are to the South-West of the top-right room?
* Let's look at the ASCII map again.
* `+` (yellow door) is at roughly (8, 9). (Assuming 0,0 bottom left).
* Room 2 is to the right of x=8.
* Points F, Q, D are North of y=9.
* Points A, C are South of y=9 (y=11,12? No, map y increases up).
* Let's count rows. Map height is 16.
* Top row is 15.
* F, Q are at y=14. D at y=13. A is at y=12. C is at y=11.
* Yellow door `+` (connecting left/right) is at y=7? No.
* Let's look at `##.....O+.....R#`. The `+` is there.
* Rows from bottom (0-indexed):
* Row 0: `################`
* Row 1: `#....B.#########`
* Row 2: `#......#########`
* Row 3: `#.N....#########`
* Row 4: `#...M..#########`
* Row 5: `#E.....#########`
* Row 6: `#.I.J..#########`
* Row 7: `######*#########` <-- Agent is here (Blue Door). y=7.
* Row 8: `##.HP.L.########`
* Row 9: `##G.....########`
* Row 10: `##.....O+.....R#` <-- Yellow Door is here? No, `+` is here. Wait.
* Row 11: `##.K....#......#`
* Row 12: `##......#C.....#`
* Row 13: `##......#...A..#`
* Row 14: `#########.D....#`
* Row 15: `#########F.Q...#`
* Okay, coordinate system check:
* Agent `*` is at y=7 (approx). This is the door between Room 1 (North) and Room 3 (South).
* Wait, the text said "Agent started in Room 1... Initial pos (0,0)... North is +y".
* Text said "blue door" on right wall (South) when facing East. This matches a door at the bottom of Room 1.
* Text said "yellow door" on front wall (East) when facing East. This matches a door on the right of Room 1.
* So Room 1 is the Top-Left room.
* Contains G, H, P, L, K, O.
* Yellow Door is at `+` (Row 10, Col 8 approx). Connects to Room 2 (Top-Right).
* Blue Door is at `*` (Row 7, Col 6 approx). Connects to Room 3 (Bottom-Left).
* Okay, now analyze coverage.
* **Room 1 (Top-Left):**
* Observed from start (0,0) facing North (saw nothing).
* Observed from start (0,0) facing East (saw shoes, rubberduck, etc).
* Start position (0,0) in Room 1 local coords. Where is that in map coords?
* Map `*` is the Blue Door. Agent is currently there.
* The Blue Door was "front-right" (South-East) from the start position when facing East.
* Start position was likely near `G` or `H`.
* When facing East from start, saw Yellow Door (East) and Blue Door (South/Right).
* This covers the area between Start and Yellow Door, and Start and Blue Door.
* Points G, H, P, L, K, O are in Room 1.
* Agent has traversed Room 1. The region is likely "explored" in the sense of finding doors.
* Have we observed points `K` and `O`? `K` is North-West-ish. `O` is near the Yellow Door.
* From Start (facing East), FOV is North-East to South-East. `K` is likely "behind" or "left" (North-West).
* From Start (facing North), FOV is North-West to North-East. `K` might have been seen if it was there? But "No objects in field of view". So `K` location was seen and empty? Or `K` is a point in space not an object.
* Wait, the question asks "Select the points that are located in unexplored/unobserved regions."
* "Unobserved region" means a grid cell that has not fallen into the FOV of any Observe() action.
* Let's trace FOVs precisely.
* **Action 1: At Start, Face North.**
* Where is Start?
* Agent faced East and saw Yellow Door (East) and Blue Door (South/Right).
* Start is roughly North-West of Blue Door and West of Yellow Door.
* Let's assume Start is near `G` or `H`.
* Facing North: Sees area above Start. (Top-Left corner).
* **Action 2: At Start, Face East.**
* Sees area to the Right. Sees Yellow Door. Sees Blue Door (front-right).
* This covers the area from Start to the East wall.
* **Action 3: At Yellow Door, Face East.**
* Looking into Room 2.
* Saw `laptop`, `airplane`, `backpack` (front-left/North). `books` (front/East).
* This covers the center and North of Room 2.
* Points F, Q, D are in the North of Room 2. Likely observed.
* Point R is in the South-East corner? Row 10 is the door row. Row 10 has `.....O+.....R#`. `R` is in the wall/corner? No, looks like inside Room 2.
* Points A (Row 13), C (Row 12).
* From Yellow Door (Row 10), facing East. FOV 90 deg (45 left, 45 right).
* Left is North (Rows 11+). Right is South (Rows 9-).
* Wait, if Agent is at Yellow Door facing East (Right on map), Left is UP (North).
* So FOV covers Rows 10 to ... and Columns > 8.
* "Front-Left" (North-East) saw laptop, airplane. This covers Rows 11, 12, 13, 14, 15?
* "Front" saw books.
* Did it see "Front-Right" (South-East)? No mention of objects.
* So the area "South" of the X-axis extending from the door (Rows < 10 in Room 2) is the "Right" side of the FOV.
* Wait, map Y increases Up.
* Yellow Door is at Row 10.
* Facing East. Left is North (Rows > 10). Right is South (Rows < 10).
* Points A (Row 13), C (Row 12), D (Row 14), F, Q (Row 15) are all NORTH of the door (Row 10).
* Wait, let's check the map visually.
* `##.....O+.....R#` is Row 10. `+` is the door. `R` is to the right.
* Rows 11-15 are ABOVE Row 10.
* So A, C, D, F, Q are in the "Left" (North) FOV of the agent at Yellow Door facing East.
* The agent saw `laptop`, `airplane`, `backpack` in "front-left".
* So the region containing A, C, D, F, Q has been observed (at least partially).
* What about R? R is at Row 10, to the right of the door. "Front". Likely observed.
* What about the area BELOW Row 10 in Room 2?
* Map shows Room 2 is only Rows 10-15?
* Look at the wall `########` at Row 9.
* Yes, Room 2 is Rows 10-15.
* So Room 2 is fully North of the door? No, the door is on the South wall of Room 2?
* If `+` is at Row 10, and Room 2 is Rows 10-15, then the door is on the bottom edge.
* Agent at `+` facing East (into the room? No, East is Right).
* If Room 2 is the block on the top right...
* Agent at `+` looking East looks ALONG the wall?
* Wait. `+` is on a Vertical wall `|` or Horizontal `-`?
* Map:
`##.....O+.....R#`
`##.K....#......#`
* The `+` is part of a horizontal structure? No, looking at `##.....O+.....R#` it looks like a horizontal wall.
* BUT, the text said "Yellow door on front wall (East)".
* If I am in Room 1 (Top Left) and look East, I see the wall dividing Room 1 and Room 2.
* So the wall must be Vertical.
* Let's re-parse the map.
`################`
`#########F.Q...#`
`#########.D....#`
`##......#...A..#`
`##......#C.....#`
`##.K....#......#`
`##.....O+.....R#`
`##G.....########`
`##.HP.L.########`
* Columns 0-1: `##` (Wall)
* Columns 2-7: Room 1 space.
* Column 8: `#` (Wall) with `+` (Door).
* Columns 9-15: Room 2 space.
* So the wall is Vertical at Column 8.
* The `+` is at (Col 8, Row 10).
* Agent at Start (in Room 1) faced East and saw it. Correct.
* Agent jumped to `+`. Facing East. Looking into Room 2.
* Room 2 spans Rows 10 to 15?
* Let's check the bottom of Room 2.
* Row 9 is `##G.....########`. Column 8 is `#`. Column 9+ is `#`. So Row 9 is a wall for Room 2.
* So Room 2 is (Cols 9-15, Rows 10-15).
* Agent at (8, 10) facing East (Towards Col 15).
* FOV: Front (East). Left (North). Right (South).
* Front covers Row 10 (Point R).
* Left (North) covers Rows 11-15 (Points C, A, D, F, Q).
* Right (South) covers Rows < 10. Room 2 doesn't exist there (Wall).
* Agent then jumped to `books`. Where are `books`? "Front, mid distance". Say (12, 10).
* Agent rotated 90 deg clockwise (Face South).
* Looking South from (12, 10).
* Saw nothing.
* South of Row 10 is the Wall (Row 9). So correct.
* **Conclusion for Room 2:** The entire room (Rows 10-15, Cols 9-15) has been covered by the FOV from the door (looking East/North-East) and potentially from `books`.
* So A, C, D, F, Q, R are LIKELY OBSERVED.

* **Room 1 (Top-Left):**
* Spans Cols 2-7. Rows 7?-15?
* Bottom of Room 1:
* Row 7: `######*#########` (Door to Room 3).
* Row 8: `##.HP.L.########`
* Row 9: `##G.....########`
* Row 10: `##.....O`...
* Room 1 seems to range from Row 7 (Door) to Row 15?
* Wait, Row 6 is `#.I.J..#########`. This is Room 3.
* So the boundary is Row 7.
* Agent started in Room 1.
* Start pos: Saw Yellow Door (Col 8, Row 10) to East. Saw Blue Door (Col 6, Row 7) to South-East.
* Start pos likely around (Col 4, Row 9)?
* Facing North (Action 1): Saw nothing. FOV covers (Col 2-6, Row 10-15).
* Facing East (Action 2): Saw Yellow Door. FOV covers (Col 5-8, Row 8-11).
* This covers `G`, `H` (maybe), `P`, `L` (maybe), `O`, `K`?
* `K` is at Row 11, Col 4.
* Start (4, 9). Facing North (Up). FOV 90 deg. Cone from (4,9) to (North).
* Covers (3,10) to (5,10), (2,11) to (6,11).
* `K` is at (4,11). Definitely in FOV of Action 1.
* Observation was "No objects". So `K` is not an object. Or I missed it?
* Wait, "You observe: No objects in field of view".
* Maybe `K` is just a point in empty space.
* But it IS observed.
* `G` (Row 9, Col 3). Start (4,9). Facing East. `G` is behind/left. Facing North. `G` is left.
* If Start is (4,9).
* Action 1 (North): G is West. Not seen.
* Action 2 (East): G is West. Not seen.
* Is `G` unexplored?
* Let's refine Start Position.
* Start facing East saw `blue door` (Row 7, Col 6) at "front-right".
* Vector from Start (x,y) to (6,7). Orientation (1,0).
* Angle must be between -45 and 0 (front-right).
* Meaning (6-x) > 0 and (7-y) < 0. So y > 7.
* And |7-y| < |6-x|. (dy < dx).
* Start facing East saw `yellow door` (Row 10, Col 8) at "front-slight-right".
* Angle between 0 and -22.5? Or Front-Right (0 to -45)?
* Wait, "front-slight-right" is (0, 22.5]. (Positive is Clockwise).
* Facing East (0 deg). Clockwise is South.
* So "front-slight-right" means slightly South of East.
* Vector to (8,10). dx > 0.
* If angle is positive (South), then target y < Start y.
* So Start y > 10.
* But if Start y > 10, then Blue Door (y=7) is WAY South. (Start y - 7).
* If Start y > 10, Blue Door is front-right (South-East). Angle?
* dx = 6-x. dy = 7-y.
* Start x approx 3 or 4?
* Let's say x=4. dx=2. dy = 7-11 = -4. Angle atan(-2) approx -63 deg (South-East).
* This would be "right" or "front-right" (within 45 deg?). 45 deg is |dx|=|dy|.
* If dy > dx, it's more South than East.
* "front-right" bin is (22.5, 45).
* "front-slight-right" bin is (0, 22.5).
* Let's check the bins again.
* Bins: [-45,-22.5) FL, [-22.5,0) FSL, 0 F, (0,22.5] FSR, (22.5,45] FR.
* Facing East.
* Yellow Door (8,10): "front-slight-right" -> Angle in (0, 22.5]. South of East.
* This implies Start Y > 10.
* Blue Door (6,7): "front-right" -> Angle in (22.5, 45]. More South.
* This implies Start Y is even larger relative to X distance.
* But Yellow Door y=10. If Start y > 10, Yellow Door is South.
* Let's test Start = (3, 11).
* To Yellow (8,10): dx=5, dy=-1. Angle atan(1/5) ~ 11 deg. (South). Fits FSR.
* To Blue (6,7): dx=3, dy=-4. Angle atan(4/3) ~ 53 deg. (South).
* 53 deg is > 45. Should be "Right" or "Beyond FOV"?
* Wait, "front-right" is up to 45.
* Maybe Start is (2, 11)? dx=6, dy=-1 (angle small). To Blue: dx=4, dy=-4 (angle 45). Fits FR.
* So Start is likely (2, 11) or (3, 11). `K` is at (4, 11).
* At (2,11).
* Action 1 (North): Covers (2,11) upwards. (2-6, 11-15).
* Action 2 (East): Covers (2,11) rightwards. (2-10, 8-14).
* Region G (3, 9)?
* From (2,11) facing East. (3,9) is dx=1, dy=-2. Angle ~63 deg South. Beyond FOV (45 deg).
* From (2,11) facing North. (3,9) is South. Behind.
* So `G` (Row 9) is likely **UNEXPLORED**.
* `H` (Row 8, Col 4). From (2,11): dx=2, dy=-3. Angle > 45. Unexplored.
* `P` (Row 8, Col 5). dx=3, dy=-3. Angle 45. Borderline.
* `L` (Row 8, Col 7). dx=5, dy=-3. Angle ~30. In FOV (Front-Right). Observed.
* So `G`, `H` seem unobserved. `P` maybe.

* **Room 3 (Bottom-Left):**
* Cols 2-8, Rows 1-6?
* Agent is at `*` (Row 7, Col 6) facing South.
* Just observed: `shoppingcart` (Front/South), `red chair` (Front-Right/South-West).
* FOV: South (Cone).
* Covers Rows 0-6. Cols:
* Straight South is Col 6.
* Front-Right (Agent facing South, Right is West). So South-West.
* Front-Left (Agent facing South, Left is East). So South-East.
* Cone covers Cols < 6 and Cols > 6 slightly?
* Let's check points.
* `I` (Row 6, Col 3). From (6,7) facing South.
* dx = 3-6 = -3. dy = 6-7 = -1.
* Relative to South: Forward 1, Right 3.
* Angle atan(3/1) = 71 deg. > 45. Beyond FOV?
* "Front-Right" max angle 45.
* So `I` is likely NOT observed.
* `J` (Row 6, Col 5). dx=-1, dy=-1. Angle 45. Borderline. Probably observed or near.
* `E` (Row 5, Col 2). dx=-4, dy=-2. Angle > 45. Not observed.
* `M` (Row 4, Col 5?). dx=-1, dy=-3. Angle small. Observed.
* `N` (Row 3, Col 3). dx=-3, dy=-4. Angle 36. Observed (Front-Right).
* `B` (Row 1, Col 6). Straight South. Observed.
* So `I`, `E` seem Unobserved.
* `J`? If angle 45, maybe.
* `M`, `N`, `B` are observed.
* What about `G`, `H` in Room 1? We decided likely Unobserved.

* **Candidate Selection:**
* Candidates: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R.
* **Room 2 (Top Right):** A, C, D, F, Q, R.
* Agent at `+` (8,10) facing East.
* Front: East.
* Left: North (Rows 11+).
* Right: South (Rows <10).
* A (Row 13), C (Row 12), D (Row 14), F (Row 15), Q (Row 15). All North-East of Agent.
* Agent saw "Front-Left" (North-East) objects.
* Assuming "Front-Left" covers the sector, these are observed.
* R (Row 10). East. Observed.
* So Room 2 candidates are OBSERVED.
* **Room 1 (Top Left):** G, H, P, L, K, O.
* Start ~ (2,11).
* Action 1 (North): Covers `K`.
* Action 2 (East): Covers `O` (Row 10, Col 8) - yes, saw Yellow Door there.
* `L` (Row 8, Col 7). dx=5, dy=-3. Angle 30. Observed.
* `P` (Row 8, Col 5). dx=3, dy=-3. Angle 45. Borderline.
* `H` (Row 8, Col 4). dx=2, dy=-3. Angle 56. Unobserved.
* `G` (Row 9, Col 3). dx=1, dy=-2. Angle 63. Unobserved.
* Unobserved candidates: **G, H**. Maybe P? Let's assume P is visible or `H` is the clear one. `G` is definitely out.
* **Room 3 (Bottom Left):** I, J, E, M, N, B.
* Agent at `*` (6,7) facing South.
* FOV South (+/- 45 deg).
* `B` (1,6). Straight South. Observed.
* `M` (4,5). South-South-West. Angle small. Observed.
* `N` (3,3). dy=4, dx=3. Angle 37. Observed.
* `J` (6,5). dy=1, dx=1. Angle 45. Borderline.
* `I` (6,3). dy=1, dx=3. Angle 71. Unobserved.
* `E` (5,2). dy=2, dx=4. Angle 63. Unobserved.
* Unobserved candidates: **I, E**.

* **Refining the list:**
* G: Unobserved (West wall of Room 1).
* H: Unobserved (South-West corner of Room 1).
* E: Unobserved (West wall of Room 3).
* I: Unobserved (North-West corner of Room 3).
* What about P? If H is unobserved, P (next to it) might be. But P is closer to the center/angle. 45 degrees is the cutoff. From (2,11) to (5,8) is exactly 45 degrees. Usually "Front-Right" includes 45. So P is likely observed. H (angle 56) is not.
* What about J? From (6,7) to (5,6) is exactly 45 degrees. Likely observed. `I` (angle 71) is not.
* What about Room 2 points?
* A, C, D, F, Q are all North of the door.
* Agent at door facing East. North is "Left".
* "Front-Left" (North-East) was reported.
* The only issue is if the agent didn't look "Left" enough.
* "Front-Left" bin is [-45, -22.5). "Front-Slight-Left" is [-22.5, 0).
* Agent saw objects in "Front-Left" and "Front-Slight-Left".
* This covers 0 to 45 degrees Left (North).
* Points F, Q are at Row 15. Door Row 10. dy=5.
* Col range 9-15. Door Col 8.
* Q at (13, 15)? dx=5, dy=5. Angle 45. Observed.
* F at (10, 15)? dx=2, dy=5. Angle atan(2/5) ~ 21 deg from North?
* Wait. Agent facing East. North is 90 deg Left.
* "Front-Left" is 22.5 to 45 deg Left.
* If something is at 90 deg Left (straight North), it is "Left" (Beyond FOV).
* Let's check angles relative to East (0 deg).
* Vector to F (10, 15) from (8,10). dx=2, dy=5.
* Angle = atan(5/2) = 68 degrees.
* 68 degrees is > 45.
* So F is in "Left" bin (Beyond FOV of Front-Left).
* Is "Left" reported? No.
* "Front-Left" objects were reported.
* So objects at > 45 deg might NOT be observed.
* F (10,15): Angle 68. Unobserved.
* Q (13,15): Angle atan(5/5) = 45. Observed.
* D (11,14): dx=3, dy=4. Angle 53. Unobserved.
* A (13,13): dx=5, dy=3. Angle 31. Observed.
* C (11,12): dx=3, dy=2. Angle 33. Observed.
* So F and D might be unobserved.
* Let's check the Observation at Yellow Door again.
* "laptop: front-left... facing forward"
* "airplane: front-left... facing right"
* "backpack: front-slight-left..."
* The report gives specific objects. It doesn't explicitly say "F is here".
* However, if F and D are just points in the room, and the sector containing them (Left/North) was not fully covered (only up to 45 deg), then they are unobserved.
* Let's re-verify the "Front-Left" definition.
* "Egocentric angle bins... [-45°,-22.5°)→front-left... otherwise→beyond-fov."
* FOV is 90 degrees total (45 left to 45 right).
* Any point with angle > 45 degrees from Front is "beyond-fov".
* Agent facing East.
* Points F (angle 68) and D (angle 53) are > 45.
* So F and D are Unobserved.
* What about Q? Angle 45. Borderline. Usually included.
* What about C? Angle 33. Included.
* What about A? Angle 31. Included.
* So **F, D** are candidates.

* **Consolidating the list:**
* Room 1: G, H.
* Room 2: F, D.
* Room 3: E, I.
* Let's check Room 3 again.
* Agent at (6,7) facing South.
* `E` (2,5)? No, `E` is at (Col 2, Row 5).
* Vector from (6,7) to (2,5). dx=-4, dy=-2.
* Facing South (0, -1).
* Vector is (-4, -2).
* Angle relative to South:
* Dot product / mags?
* Simple way: relative to South, (2,5) is "Forward 2, Right 4".
* Angle = atan(4/2) = 63 deg. > 45.
* So E is Unobserved.
* `I` (Col 3, Row 6).
* Vector (-3, -1). Forward 1, Right 3. Angle atan(3/1) = 71 deg.
* So I is Unobserved.
* `J` (Col 5, Row 6).
* Vector (-1, -1). Angle 45. Observed.

* **Final Candidate Set:** D, E, F, G, H, I.

* **Double Check:**
* Did we miss any observations?
* Room 1 was observed facing North (Start) and East (Start).
* Start (2,11).
* Face North covers (2,11) to (6,15).
* Face East covers (2,11) to (10,3)? No, cone opens right.
* Upper limit of East cone: +45 deg (South-East). Line y = 11 - (x-2).
* At x=3, y=10. At x=4, y=9. At x=5, y=8.
* G is at (3,9). On boundary?
* Line: y = 13 - x.
* Check G(3,9): 9 vs 13-3=10. 9 < 10. Inside cone?
* East cone is bounded by y = y0 + (x-x0) and y = y0 - (x-x0).
* Bounded by y = 11 + (x-2) = x+9 and y = 11 - (x-2) = 13-x.
* For G(3,9): y=9. Lower bound is 13-3=10.
* Since 9 < 10, G is OUTSIDE the East-facing cone (too far South).
* G is also South of the North-facing cone.
* So G is Unobserved. Correct.
* Check H(4,8):
* Lower bound y = 13-4 = 9.
* y=8. 8 < 9. Outside.
* H is Unobserved. Correct.
* Check P(5,8):
* Lower bound y = 13-5 = 8.
* y=8. On boundary. Usually inclusive? Or "Front-Right" is (22.5, 45].
* If P is observed, good. If not, it should be in the list.
* Let's stick to the clear ones: G, H.
* Room 2 was observed from (8,10) facing East.
* Cone: y = 10 +/- (x-8).
* Upper bound (Left/North): y = 10 + (x-8) = x + 2.
* Check F(10,15): y=15. Bound = 10+2 = 12.
* 15 > 12. F is Outside (too far North/Left).
* F is Unobserved. Correct.
* Check D(11,14): y=14. Bound = 11+2 = 13.
* 14 > 13. D is Outside.
* D is Unobserved. Correct.
* Check A(13,13): y=13. Bound = 13+2 = 15.
* 13 < 15. A is Inside. Observed.
* Room 3 was observed from (6,7) facing South.
* Cone: dx <= dy (Forward is -y). |x - 6| <= |y - 7|.
* Check E(2,5): |2-6| = 4. |5-7| = 2. 4 <= 2 is False.
* E is Outside. Unobserved. Correct.
* Check I(3,6): |3-6| = 3. |6-7| = 1. 3 <= 1 is False.
* I is Outside. Unobserved. Correct.

* **Resulting List:** D, E, F, G, H, I.
* Let's quickly check `K`.
* Start (2,11). Face North. Cone |x-2| <= y-11.
* K(4,11): |4-2| = 2. y-11 = 0. 2 <= 0 False.
* K is Outside North FOV?
* Wait. If K is at same y, it's 90 degrees right. "Right" is not in "Front" FOV.
* Face East. Cone |y-11| <= x-2.
* K(4,11): |11-11| = 0. x-2 = 2. 0 <= 2 True.
* K is straight East.
* So K is Observed in Action 2.
* Okay, K is observed.

* What about Q?
* From (8,10) East. Cone |y-10| <= x-8.
* Q(13,15). |15-10|=5. x-8=5. 5<=5. True.
* Q is Observed.

* Are there any other points?
* L(7,8) from Start(2,11) East?
* |8-11|=3. 7-2=5. 3<=5. True. Observed.
* M(5,4) from BlueDoor(6,7) South?
* |5-6|=1. |4-7|=3. 1<=3. True. Observed.
* N(3,3) from BlueDoor(6,7) South?
* |3-6|=3. |3-7|=4. 3<=4. True. Observed.

* **Final check:**
* Room 1 Unobserved: G, H.
* Room 2 Unobserved: D, F.
* Room 3 Unobserved: E, I.
* Total: D, E, F, G, H, I.

* Wait, is `P` observed?
* P(5,8). Start(2,11). Face East.
* Cone: |y-11| <= x-2.
* |8-11| = 3. 5-2 = 3. 3 <= 3. True.
* P is Observed.

* Okay, the list D, E, F, G, H, I seems solid.

FINAL ANSWER:
```json
{
"unexplored": ["D", "E", "F", "G", "H", "I"]
}
```

THINK:
1. **Analyze the current state:**
* Agent is at the `blue door` (marked as `*` on the map).
* Agent is facing South (down on the map).
* Agent just observed Room 3 (South of the blue door).
* Objects observed in Room 3: `shoppingcart` (front/South, slightly far), `red...

################
#########F.Q...#
#########.D....#
##......#...A..#
##......#C.....#
##.K....#......#
##.....O+.....R#
##G.....########
##.HP.L.########
######*#########
#.I.J..#########
#E.....#########
#...M..#########
#.N....#########
#......#########
#....B.#########
################

You jumped to blue door. You observe:
• shoppingcart: front, slightly far, facing forward
• red chair: front-right, mid distance, facing forward.
You have a maximum of 13 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to blue door. You observe:
• shoppingcart: front, slightly far, facing forward
• red chair: front-right, mid distance, facing forward.
You have a maximum of 13 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at the "blue door" facing South, looking into Room 3.
1. Objects observed: "shoppingcart" (front) and "red chair" (front-right).
2. The area to the left (East side of Room 3) and deeper right (West side) might not be fully covered.
3. To explore Room 3 more thoroughly, the agent should enter the room.
4. Jumping to the "shoppingcart" (front) seems like a good central position to pivot from.
5. From the "shoppingcart", rotating to scan the room is necessary. Since "red chair" was front-right, rotating right (West) or left (East) could reveal more. Let's try to capture the rest of the room. The agent is facing South. Rotating 90 degrees clockwise will face West. Rotating -90 degrees counter-clockwise will face East. Let's rotate -90 to face East (left from current view) to check that corner, or perhaps just observing from the new position is enough first? No, the goal is to reveal unknowns.
6. The agent sees shoppingcart (South) and red chair (South-West relative to door? No, front-right is South-West). Wait, facing South: Front=South, Right=West. So red chair is South-West.
7. Let's jump to "shoppingcart". Then rotate to look at the unobserved areas.
8. Current FOV covered South (front) and South-West (front-right). The area to the South-East (front-left) is unobserved.
9. Therefore, after jumping to "shoppingcart", rotating -90 degrees (counter-clockwise) to face East would reveal the area that was to the left of the door.

The agent is at the "blue door" facing South, looking into Room 3.
1. Objects observed: "shoppingcart" (front) and "red chair" (front-right).
2. The area to the left (East side of Room 3) and deeper right (West side) might not be fully covered.
3. To explore Room 3 more thoroughly, the agent shou...

THINK:
The agent started at (0,0) in Room 1 facing North.
1. **Room 1:**
* Agent at (0,0) facing North: Observed nothing.
* Agent at (0,0) facing East:
* "shoes": front-slight-right (East-South), slightly far. facing backward (West).
* "rubberduck": front-right (South-East), mid. facing left (North).
* "alarmclock": front-left (North-East), mid. facing backward (West).
* "yellow door": front-slight-right (East), slightly far, on front wall (East wall).
* "blue door": front-right (South), slightly far, on right wall (South wall).
* Relative relations: shoes is North of rubberduck, South of yellow door. Rubberduck is East of alarmclock.
* Coordinates estimation (Origin 0,0):
* Facing East, front is +x. Right is -y. Left is +y.
* "alarmclock" (front-left): +x, +y.
* "yellow door" (front): +x. Let's say (6,0).
* "blue door" (front-right): +x, -y. Wait, on "right wall" implies it's on the South wall. If agent is at (0,0) facing East, right is South. The door is "front-right".
* "shoes" (front-slight-right): +x, slight -y? "shoes is south, near to yellow door". So if yellow door is at y=0, shoes is at y=-2.
* "rubberduck" (front-right): +x, -y.
2. **Room 2 (East of Room 1):**
* Agent jumped to "yellow door" (facing East).
* Observed:
* "laptop": front-left (North-East), slightly far. facing forward (East?? No, relative to object? usually "facing forward" means facing the agent? Or facing its own front? Instructions: "facing forward/backward/right/left (ego) or north/east/south/west (allo)". The observation says "facing forward". Let's assume allo for map if possible, but the observations are ego. Wait, the first observation said "facing backward". If I am facing East, backward is West. Here "facing forward" likely means facing the same direction as agent? Or facing the agent (West)? Usually "facing forward" for an object implies its front is towards the viewer, i.e., facing West. Or aligned with agent? Let's stick to positions first.
* "airplane": front-left (North-East), slightly far.
* "backpack": front-slight-left (East-North), slightly far.
* "books": front (East), mid distance.
* Agent jumped to "books" (facing East, then rotated to South). "books" is East of "yellow door".
* Rotated to face West (back to door): "yellow door" is front.
3. **Room 3 (South of Room 1?):**
* Agent jumped back to "yellow door" (facing West). Rotated to South.
* Observed "blue door" (front-right).
* Jumped to "blue door". Facing South.
* Observed:
* "shoppingcart": front (South), slightly far.
* "red chair": front-right (South-West), mid.
* Jumped to "shoppingcart" (facing South). Rotated to East. Observed nothing.

**Coordinate Estimation:**
* **Agent Start:** (0,0) facing North.
* **Room 1:**
* Rotated East.
* **Yellow Door:** East of (0,0). Distance "slightly far" (4-8). Let's pick x=6, y=0.
* **Blue Door:** South-East of (0,0). Distance "slightly far". "On right wall" (South wall). Let's pick x=3, y=-4? Or x=4, y=-4.
* **Shoes:** Near yellow door, south of it. (6, -2).
* **Rubberduck:** South of shoes? "shoes is north, near to rubberduck". So rubberduck is (6, -4).
* **Alarmclock:** North-West of rubberduck? "rubberduck is east, near to alarmclock". So alarmclock is (4, -4). Wait, alarmclock was "front-left" from (0,0) facing East. That means North-East. So (x>0, y>0). This contradicts "rubberduck is east of alarmclock" if rubberduck is at y=-4. Let's re-read: "rubberduck: front-right (SE)", "alarmclock: front-left (NE)". Yes. Relation: "rubberduck is east, near to alarmclock". This implies rubberduck is East of alarmclock. If alarmclock is at y=1, rubberduck at y=-4, then rubberduck is South-East. The "near" relation is tricky. Let's trust the "front-left" vs "front-right" more. Alarmclock ~ (4, 2). Rubberduck ~ (4, -2).
* **Room 2:**
* Entered via Yellow Door (6,0). Facing East.
* **Books:** Front (East). Mid distance (2-4). Let's say (10, 0).
* **Laptop:** Front-left (NE). (10, 3).
* **Airplane:** Front-left (NE). (9, 4).
* **Backpack:** Front-slight-left (ENE). (9, 2).
* **Room 3:**
* Entered via Blue Door. Let's place Blue Door at (3, -5) on the South wall of Room 1? Or (6, -5)?
* From Yellow Door (6,0) facing West, rotated South (-90? No, West to South is Left, i.e., +90? No. Agent at Yellow Door (6,0) facing West. Rotated -90 (counter-clockwise). West -> South. Correct.
* Saw Blue Door at "front-right". Facing South, front is South, Right is West. So Blue Door is South-West of Yellow Door (6,0).
* Let's place Blue Door at (2, -5).
* Jumped to Blue Door (2, -5). Facing South.
* **Shoppingcart:** Front (South). Slightly far (4-8). (2, -10).
* **Red Chair:** Front-right (South-West). (0, -8).
* Agent is currently at "shoppingcart" (2, -10), facing East.

**Refining Coordinates:**
* Agent: (2, -10) (at shoppingcart). Facing: East.
* Yellow Door: (6, 0).
* Blue Door: (2, -5).
* Shoes: (6, -1) (South of Yellow Door).
* Rubberduck: (6, -3) (South of Shoes).
* Alarmclock: (4, -3) (West of Rubberduck). Checks out with "front-left" from (0,0) facing East? No, front-left is NE. (4, -3) is SE.
* Let's re-read Room 1 obs from (0,0) facing East.
* Alarmclock: front-left (NE).
* Rubberduck: front-right (SE).
* Relation: "rubberduck is east, near to alarmclock". If Alarmclock is NE (e.g. 3, 1) and Rubberduck is SE (e.g. 5, -1), Rubberduck is East-South. "Near" (dist <= 2). Distance between (3,1) and (5,-1) is sqrt(4+4) = 2.8 > 2. Maybe (3, 0.5) and (4.5, -0.5)?
* Let's assume Alarmclock is at (3, 1) and Rubberduck is at (4, 0).
* Shoes is "north, near to rubberduck". Rubberduck at (4,0) -> Shoes at (4, 1.5).
* Shoes is "south, near to yellow door". Yellow door at (6,0). Shoes at (6, -1)? If Shoes is South of Yellow Door, and North of Rubberduck, then Yellow Door > Shoes > Rubberduck in Y.
* Yellow Door (6, 0). Shoes (6, -2). Rubberduck (6, -4).
* Alarmclock: West of Rubberduck? "rubberduck is east, near to alarmclock". So Alarmclock is West. (4, -4).
* Does this fit "front-left" for Alarmclock from (0,0) facing East? Facing East, Front-Left is North-East. (4, -4) is South-East.
* Contradiction.
* Let's look at "front-left" again. Agent facing East. Front is East. Left is North. Front-Left is NE.
* Alarmclock MUST be +y.
* Then Rubberduck is East of it (larger x) and near. So Rubberduck is +y (or close to 0).
* But Rubberduck is "front-right" (SE). So Rubberduck is -y.
* If Alarmclock is y=0.5 and Rubberduck is y=-0.5. They are near.
* Let's put Alarmclock (4, 1). Rubberduck (5, -1). Distance ~2.2.
* Shoes is North of Rubberduck. (5, 1).
* Shoes is South of Yellow Door. Yellow Door (5, 3)?
* Yellow Door was "front-slight-right" (East-South) from (0,0). So Yellow Door y < 0.
* This implies "Alarmclock front-left" is the outlier or I'm misinterpreting "front-left" range. Range: [-45, -22.5). Facing East (0 deg). -22.5 is slight left. -45 is Left. Wait.
* Rotated 90 deg clockwise. North -> East.
* Bearing logic: 0 is front. + is clockwise (Right). - is counter-clockwise (Left).
* Front-left: [-45, -22.5). Negative angle. Left.
* Facing East. Left is North. So NE quadrant. Correct.
* Front-right: (22.5, 45]. Positive angle. Right. SE quadrant. Correct.
* Yellow Door: Front-slight-right. (0, 22.5]. Slight South. y < 0.
* So Yellow Door is at y < 0.
* Shoes: South of Yellow Door. y_shoes < y_door.
* Rubberduck: South of Shoes. y_duck < y_shoes.
* So all are in SE quadrant.
* How can Alarmclock be Front-Left (NE) and Rubberduck (SE) be "East, near to Alarmclock"?
* Maybe Alarmclock is at y=0.5 (NE) and Rubberduck is at y=-0.5 (SE). They are adjacent vertically? No, East relation means similar y, different x.
* "Rubberduck is East... to Alarmclock". Means Rubberduck x > Alarmclock x.
* If Alarmclock is (4, 0.1) and Rubberduck is (5, -0.1). They are near. Alarmclock is front-left (just barely). Rubberduck is front-right (just barely).
* This works.
* Yellow Door: Front-slight-right. x=6, y=-1.
* Shoes: South of Yellow Door. x=6, y=-2.
* Rubberduck: x=6, y=-3.
* Alarmclock: West of Rubberduck (so x<6) and near. x=5, y=-3?
* If Alarmclock is (5, -3), from (0,0) facing East, angle is atan(-3/5) = -30 deg. -30 is in [-45, -22.5) -> Front-Left?
* Facing East (0 deg global? No, 0 is front).
* Agent facing East. Target (5, -3). Vector (5, -3).
* Angle relative to front (East): atan2(-3, 5) = -30.9 degrees.
* Bins: [-45, -22.5) is front-left.
* -30.9 fits "front-left".
* Wait, is negative clockwise or counter-clockwise?
* "Bearing is a degree... +: clockwise, -: counterclockwise."
* Facing East. (5, -3) is to the Right. Right is Clockwise (+).
* So (5, -3) should be +30 degrees. +30 falls in (22.5, 45] -> front-right.
* So Alarmclock at (5, -3) would be front-right.
* Observation says Alarmclock is "front-left".
* Front-left is Counter-Clockwise (-). Facing East, CCW is North.
* So Alarmclock MUST have y > 0.
* Let's restart coordinates.
* Alarmclock: (4, 1). Angle atan(1/4) = 14 deg (Left/CCW). Fits "front-slight-left"? No, front-slight-left is [-22.5, 0). 14 is in that range? -14 is. +14 is Right?
* Let's stick to the bins.
* Bin 0: Front. [-22.5, 0) and (0, 22.5]? No.
* "Egocentric angle bins (0° is front): [-45°,-22.5°)→front-left, [-22.5°,0°)→front-slight-left, 0°→front, (0°,22.5°]→front-slight-right, (22.5°,45°]→front-right"
* Negative is CCW (Left). Positive is CW (Right).
* Alarmclock: front-left -> Angle in [-45, -22.5). Meaning distinct Left. y > 0.
* Rubberduck: front-right -> Angle in (22.5, 45]. Meaning distinct Right. y < 0.
* Yellow Door: front-slight-right -> Angle in (0, 22.5]. Slight Right. y < 0 (small).
* Shoes: "south, near to yellow door".
* Rubberduck: "east, near to alarmclock". This is the hard constraint.
* If Alarmclock is at y > 0 (e.g. y=3) and Rubberduck is at y < 0 (e.g. y=-3), they cannot be "near" (dist <= 2).
* Unless the "East" relation is allo-centric (Cardinal).
* "Cardinal angle bins (45° each): ... (67.5°,112.5°]→east ..."
* "rubberduck is east, near to alarmclock".
* This means the vector from Alarmclock to Rubberduck is roughly East. (dx > 0, dy ~ 0).
* This implies Rubberduck and Alarmclock have similar y coordinates.
* Contradiction with egocentric observations from (0,0) facing East?
* Maybe the agent isn't at (0,0)? "Unless otherwise specified... (0,0)".
* Maybe I mapped "front-left" wrong?
* Facing East. Front is +x. Left is +y. Right is -y.
* Alarmclock (Front-Left) -> +y.
* Rubberduck (Front-Right) -> -y.
* They cannot be near and east-west aligned if one is +y and one is -y (unless y is very small, but angles are large).
* Angle > 22.5 means |y|/x > tan(22.5) ~ 0.41.
* If x=4. y_alarm > 1.6. y_duck < -1.6. Dist_y > 3.2. Not near.
* Is it possible "front-left" means something else? No.
* Is it possible "rubberduck is east, near to alarmclock" is wrong? No, provided in prompt.
* Maybe "Observe()" list order matters?
* Maybe the "north" in "Assume your current facing direction is called 'north'" changes things?
* "Assume your current facing direction is called 'north'": This implies the relative descriptions (shoes is north...) are based on the agent's facing direction being the reference North.
* Agent facing East. So "North" (relative) = East (global). "South" (relative) = West (global). "East" (relative) = South (global).
* "rubberduck is east, near to alarmclock". Relative East = Global South.
* So Rubberduck is SOUTH of Alarmclock.
* Let's check: Alarmclock (+y), Rubberduck (-y). Rubberduck is indeed South of Alarmclock.
* Distance? If Alarmclock is (4, 1.7) and Rubberduck is (4, -1.7). Dist = 3.4. Mid distance (2-4).
* Prompt says "near" (<= 2).
* Maybe x is small? If x=2. y > 0.8. y < -0.8. Dist > 1.6.
* If x=2, y=0.9 (Alarm) and y=-0.9 (Duck). Dist=1.8 (Near).
* Angle atan(0.9/2) = 24 deg.
* Alarm: 24 deg Left (Front-Left? -22.5 to -45). Yes, -24 fits.
* Duck: 24 deg Right (Front-Right? 22.5 to 45). Yes, +24 fits.
* So: x=2. Alarmclock (2, 1). Rubberduck (2, -1).
* Yellow Door: Front-slight-right. (0, 22.5]. x=6 (slightly far). y in [0, -2.4].
* Shoes: "north, near to rubberduck". Relative North = Global East. Shoes is East of Rubberduck.
* Shoes: "south, near to yellow door". Relative South = Global West. Shoes is West of Yellow Door.
* So: Rubberduck (2, -1) < Shoes < Yellow Door (6, y_door).
* Shoes at (4, -1)?
* Yellow Door at (6, -1)?
* Angle of Yellow Door (6, -1): atan(-1/6) = -9 deg (Right/CW). 9 deg fits "front-slight-right".
* This works!
* **Revised Coordinates Room 1:**
* Agent (0,0).
* Alarmclock: (2, 1).
* Rubberduck: (2, -1).
* Shoes: (4, -1).
* Yellow Door: (6, -1).
* Blue Door: Front-right (22.5 to 45). Slightly far. On right wall (South).
* Let's say Blue Door is at (4, -4). Angle atan(-4/4) = -45 (Right). Borderline.
* Or (3, -5).

* **Room 2:**
* Jumped to Yellow Door (6, -1). Facing East.
* "laptop": Front-left (NE). Slightly far.
* "airplane": Front-left (NE). Slightly far.
* "backpack": Front-slight-left (ENE). Slightly far.
* "books": Front (E). Mid.
* Relations (Agent facing East -> North_rel=East_glob):
* "laptop is south, near to backpack". South_rel=West_glob. Laptop is West of Backpack.
* "laptop is west, near to books". West_rel=North_glob. Laptop is North of Books.
* "airplane is west, near to backpack". West_rel=North_glob. Airplane is North of Backpack.
* Let's place Books at (10, -1) (Front, mid).
* Laptop is North of Books -> (10, 1).
* Laptop is West of Backpack -> Backpack is East of Laptop -> (12, 1).
* Airplane is North of Backpack -> (12, 3).
* Let's check FOV from (6, -1) facing East:
* Books (10, -1): dx=4, dy=0. Angle 0. Front. OK.
* Laptop (10, 1): dx=4, dy=2. Angle atan(2/4)=26 (Left). Front-Left (Left > 22.5). OK.
* Backpack (12, 1): dx=6, dy=2. Angle atan(2/6)=18 (Left). Front-slight-left. OK.
* Airplane (12, 3): dx=6, dy=4. Angle atan(4/6)=33 (Left). Front-left. OK.
* Matches perfectly.

* **Room 3:**
* Jump to Yellow Door (6, -1). Face South.
* Blue Door is "front-right".
* Facing South. Front=South (-y). Right=West (-x).
* Front-Right is SW.
* Yellow Door is at (6, -1).
* Blue Door must be South-West of (6, -1).
* Previously estimated Blue Door at (3, -5).
* Vector from (6, -1) to (3, -5) is (-3, -4).
* Facing South (0, -1).
* Angle: atan(dx/dy). Vector in agent frame (Forward=South, Right=West).
* Forward component: 4. Right component: 3.
* Angle atan(3/4) = 37 deg (Right). Fits Front-Right (22.5 - 45).
* Distance 5 (Slightly far). OK.
* Blue Door at (3, -5).
* Jump to Blue Door (3, -5). Facing South.
* "shoppingcart": front (South). Slightly far. (3, -10).
* "red chair": front-right (SW). Mid. (1, -7).
* Agent jumped to Shoppingcart (3, -10). Rotated East. Observed nothing.

**Final Map Construction:**
* **Agent:** (3, -10) Facing East.
* **Room 1:**
* alarmclock: (2, 1)
* rubberduck: (2, -1)
* shoes: (4, -1)
* yellow door: (6, -1)
* blue door: (3, -5)
* **Room 2:**
* books: (10, -1)
* laptop: (10, 1)
* backpack: (12, 1)
* airplane: (12, 3)
* **Room 3:**
* shoppingcart: (3, -10)
* red chair: (1, -7)

Facing directions of objects (from observations):
* shoes: facing backward (West)
* rubberduck: facing left (North)
* alarmclock: facing backward (West)
* laptop: facing forward (East - relative to agent facing East? "facing forward" usually means facing the viewer in some contexts, or facing same direction. Let's assume allo East based on agent facing East). Observation: "facing forward" when agent facing East. So East.
* airplane: facing right (South - relative to agent facing East).
* backpack: facing left (North - relative to agent facing East).
* shoppingcart: facing forward (South - relative to agent facing South).
* red chair: facing forward (South - relative to agent facing South).

Wait, "facing forward" in observation usually means "facing the agent" (rotated 180) or "facing same direction"?
Instruction: "forward/backward/right/left (ego) or north/east/south/west (allo)".
"When agent faces north: forward = north".
So "facing forward" means facing the direction the agent is facing.
* Shoes (Agent East): facing backward -> West.
* Rubberduck (Agent East): facing left -> North.
* Alarmclock (Agent East): facing backward -> West.
* Laptop (Agent East): facing forward -> East.
* Airplane (Agent East): facing right -> South.
* Backpack (Agent East): facing left -> North.
* Shoppingcart (Agent South): facing forward -> South.
* Red chair (Agent South): facing forward -> South.

Refined Map:
{
"grid": "N*M", // Not required in JSON, just list objects.
"agent": {"position": [3, -10], "facing": "east"},
"alarmclock": {"position": [2, 1], "facing": "west"},
"rubberduck": {"position": [2, -1], "facing": "north"},
"shoes": {"position": [4, -1], "facing": "west"},
"yellow door": {"position": [6, -1]},
"blue door": {"position": [3, -5]},
"books": {"position": [10, -1]}, // No facing given
"laptop": {"position": [10, 1], "facing": "east"},
"backpack": {"position": [12, 1], "facing": "north"},
"airplane": {"position": [12, 3], "facing": "south"},
"shoppingcart": {"position": [3, -10], "facing": "south"},
"red chair": {"position": [1, -7], "facing": "south"}
}

Wait, "pan" and "desklamp" from the prompt list (1-12) were not found.
Pan (7), Desklamp (11).
Where could they be?
Room 1: Observed North (Empty), East (Items). West and South?
Agent at (0,0) facing North (Empty).
Rotated 90 (East). Saw items.
Rotated -90 (North). Back to start.
From Yellow Door (6, -1) facing West (looking into Room 1). Observed nothing?
"You rotated clockwise 90° (to West). You observe: yellow door". Wait, jump to books, rotate 90 (South). Empty. Rotate 90 (West). Saw Yellow Door.
Jumped to Yellow Door. Rotated -90 (South). Saw Blue Door.
Room 1's West side and North-West side might be empty or missed.
Room 3's East side? Jumped to shoppingcart, rotated -90 (East). Empty.
Room 2's South side? Jumped to books, rotated 90 (South). Empty.

The prompt asks for the map of "observed objects". I should only include what I saw.
The prompt mentions objects 1-12. I found:
1: shoes
2: shoppingcart
3: laptop
4: rubberduck
5: bike (NOT FOUND)
6: airplane
7: pan (NOT FOUND)
8: alarmclock
9: red chair
10: backpack
11: desklamp (NOT FOUND)
12: books

Did I miss any checks?
Room 1: Initial Observe North (Empty). Rotate East (Found stuff). Then left Room 1.
I never looked West or South in Room 1 from the start.
However, I returned to Yellow Door (East wall) and looked West (saw nothing but door? Wait. "You observe: yellow door..."). This implies no objects in the cone facing West from the door. This covers the central strip of Room 1.
I returned to Yellow Door and looked South (saw Blue Door).
I never looked North from the Yellow Door (North-West of Room 1).
I never looked West from the Blue Door (South-West of Room 1).
So "bike", "pan", "desklamp" might be in Room 1 (West/South) or Room 3 (West) or Room 2 (North/South hidden).
But the task is to output the map of *observed* objects.

Final check on coordinates.
Agent at (3, -10).
Action history:
1. Start (0,0) N. Obs (Empty).
2. Rot 90 -> E. Obs (shoes, duck, clock, yellow, blue).
3. Jump Yellow. (6, -1). Obs (laptop, plane, pack, books).
4. Jump Books. (10, -1). Rot 90 -> S. Obs (Empty).
5. Rot 90 -> W. Obs (Yellow door).
6. Jump Yellow. (6, -1). Rot -90 -> S. Obs (Blue door).
7. Jump Blue. (3, -5). Obs (cart, chair).
8. Jump Cart. (3, -10). Rot -90 -> E. Obs (Empty).

All looks consistent.

One detail: "red chair: front-right, mid distance".
From Blue Door (3, -5) facing South.
Front-Right is SW.
(1, -7) is SW. Distance sqrt(4+4) = 2.8 (Mid). Correct.
"facing forward" -> South.

One detail: "shoppingcart: front, slightly far".
From Blue Door (3, -5) facing South.
(3, -10) is South. Dist 5 (Slightly far). Correct.
"facing forward" -> South.

One detail: "books: front, mid".
From Yellow Door (6, -1) facing East.
(10, -1) is East. Dist 4 (Mid). Correct.

One detail: "airplane: front-left, slightly far".
From Yellow Door (6, -1) facing East.
(12, 3) is NE. Dist sqrt(36+16) = 7.2 (Slightly far). Correct.

One detail: "backpack: front-slight-left, slightly far".
From Yellow Door (6, -1) facing East.
(12, 1). Angle atan(2/6) = 18 deg. Slight left. Dist sqrt(36+4) = 6.3. Correct.

One detail: "laptop: front-left, slightly far".
From Yellow Door (6, -1) facing East.
(10, 1). Angle atan(2/4) = 26 deg. Left. Dist sqrt(16+4) = 4.5. Slightly far. Correct.

One detail: "shoes: front-slight-right, slightly far".
From (0,0) facing East.
(4, -1). Angle atan(-1/4) = -14 deg (Right). Slight right. Dist 4.1. Slightly far. Correct.

One detail: "rubberduck: front-right, mid".
From (0,0) facing East.
(2, -1). Angle atan(-1/2) = -26 deg (Right). Right. Dist 2.2. Mid. Correct.

One detail: "alarmclock: front-left, mid".
From (0,0) facing East.
(2, 1). Angle atan(1/2) = 26 deg (Left). Left. Dist 2.2. Mid. Correct.

The map seems robust.

FINAL ANSWER:
{
"agent": {"position": [3, -10], "facing": "east"},
"alarmclock": {"position": [2, 1], "facing": "west"},
"rubberduck": {"position": [2, -1], "facing": "north"},
"shoes": {"position": [4, -1], "facing": "west"},
"yellow door": {"position": [6, -1]},
"blue door": {"position": [3, -5]},
"books": {"position": [10, -1]},
"laptop": {"position": [10, 1], "facing": "east"},
"backpack": {"position": [12, 1], "facing": "north"},
"airplane": {"position": [12, 3], "facing": "south"},
"shoppingcart": {"position": [3, -10], "facing": "south"},
"red chair": {"position": [1, -7], "facing": "south"}
}

THINK:
The agent started at (0,0) in Room 1 facing North.
1. **Room 1:**
* Agent at (0,0) facing North: Observed nothing.
* Agent at (0,0) facing East:
* "shoes": front-slight-right (East-South), slightly far. facing backward (West).
* "rubberduck": front-right (Sout...

{
  "agent": {
    "position": [
      3,
      -10
    ],
    "facing": "east"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ]
  },
  "blue door": {
    "position": [
      3,
      -5
    ]
  },
  "books": {
    "position": [
      10,
      -1
    ]
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      3,
      -10
    ],
    "facing": "south"
  },
  "red chair": {
    "position": [
      1,
      -7
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "east"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "east"
  }
}

THINK: The agent is at the "shoppingcart" facing East. The observation returned "No objects in field of view". This means the local cognitive map should contain an empty "objects" dictionary, as there are no objects or doors currently visible to the agent.

FINAL ANSWER:
{
"origin": "agent",
"objects": {}
}

THINK: The agent is at the "shoppingcart" facing East. The observation returned "No objects in field of view". This means the local cognitive map should contain an empty "objects" dictionary, as there are no objects or doors currently visible to the agent.

FINAL ANSWER:
{
"origin": "agent",
...

{
  "origin": "agent",
  "objects": {}
}

{
  "origin": "agent",
  "objects": {}
}

THINK:
The agent is currently at the position marked '*' on the map, which corresponds to the "shoppingcart".
The map shows the layout of the rooms.
The agent started in Room 1 (middle-left room on map).
It moved to Room 2 (top-right room) via the "yellow door" ('+').
It then moved to Room 3 (bottom room) via the "blue door" ('+').
The agent is currently in Room 3 facing East.
The agent just observed facing East and saw nothing.
Previous observation in Room 3 from the "blue door" (facing South) revealed "shoppingcart" and "red chair" (to the front-right/West).
Let's analyze the points:
- Room 1 (middle-left): The agent started here and observed North and East. It saw the yellow door (East wall) and blue door (South wall). It saw shoes, rubberduck, alarmclock. Points E, G, F, R, J, C seem to be in Room 1. The agent faced North (saw nothing initially?), then East (saw shoes, rubberduck, alarmclock). The area to the West and North-West of Room 1 might be less explored, but the initial observation was North and saw nothing? Wait, the first action was Observe() facing North and saw "No objects". Then rotated to East. This implies the North part of Room 1 is empty or walls. Point E is in the North-West corner. G is North-East.
- Room 2 (top-right): The agent entered via the yellow door, jumped to "books", and rotated South. It saw laptop, airplane, backpack. Points P, A, M, L, K, Q are in Room 2. The agent jumped to books (likely near K or Q?) and looked South (saw nothing). The area North of the books (P, A, M) hasn't been directly faced? When at the yellow door facing East, it saw laptop, airplane, backpack to the front-left (North-East). It jumped to books (Front/East). Then looked South. The Northern part (P, A, M) was in the "front-left" periphery from the door, but might not be fully "observed" in the sense of a dedicated look, but they were listed. However, usually points marked as candidates are explicitly asking about coverage. If I saw them, they are observed. If they are in the shadow or behind, they are unexplored. P, A, M look like they are in the North part of Room 2. The agent was at the door (East side of Room 1/West side of Room 2) looking East. It saw things to the North-East. So P, A, M might have been covered.
- Room 3 (bottom): The agent is at '*' (shoppingcart). It looked South from the door (saw shoppingcart, red chair). It is now facing East and sees nothing. The points D, O, B are in the West/South-West part of Room 3. The agent looked South from the door (top of Room 3). The shoppingcart is likely central. The red chair was front-right (South-West). So B, D, O area was partially seen. Point I, N are South of the agent. H is East. The agent just looked East and saw nothing, so H is observed (as empty). The agent hasn't looked West from inside the room, nor North (back at the door). However, the initial view from the door (facing South) covered the cone towards South. The West side (D, O) was "front-right".
- Let's look at the specific points:
- A, M, P: North end of Room 2. Agent at door saw "laptop: front-left", "airplane: front-left", "backpack: front-slight-left". These are in the North-East direction. Agent jumped to books (East) and turned South. It never looked strictly North or West inside Room 2. However, the view from the door might have covered A and M. P is in the far corner.
- L, K, Q: Middle of Room 2. "books" was "front". Agent jumped there. These are likely visited/seen.
- E, G, C, F, R, J: Room 1. Agent at (0,0) looked North (saw nothing), then East (saw doors, objects). (0,0) is likely near C or F? If North is +y, and agent saw nothing North, then walls are close or empty. Then rotated East. Saw yellow door (East wall) and blue door (South wall). This implies agent is in the North-West or West part of Room 1. If Blue door is on Right (South) wall when facing East, and Yellow door is on Front (East) wall.
- D, O, B, I, N, H: Room 3. Agent at '*' (shoppingcart). Just looked East (saw nothing). H is East. So H is observed. I, N are South. Agent at door looked South. Saw shoppingcart (front) and red chair (front-right). I and N are likely "behind" the shoppingcart relative to the door? Or further South? If shoppingcart is "slightly far", and room is big, there might be space behind. But usually "slightly far" covers a good chunk. D, O, B are West. From door (facing South), front-right is South-West. Red chair was there. The agent hasn't looked strictly West from the shoppingcart.
- Logic check on "Unexplored": Usually means areas not covered by the FOV cones of any observation.
- Room 1: Agent at (0,0). Obs 1: North. Saw nothing. Covered North cone. Obs 2: East. Saw objects. Covered East cone. South and West cones from (0,0) are unobserved. BUT, the agent moved to the yellow door and looked WEST into Room 1 later? No, it looked West from "books" (in Room 2) to see the yellow door, then jumped to yellow door. At yellow door (which is between rooms), it rotated -90 to face South. It saw the blue door. It did NOT look West into Room 1 from the yellow door. It looked South. So the West part of Room 1 (behind the starting position or to the left of start) is largely unseen? Wait, start was (0,0). North seen. East seen. West and South not seen from (0,0). However, the map shows Room 1 is the one with E, G, etc. If (0,0) is bottom-left of Room 1? If so, North sees E, G. East sees J, doors. C, D? No D is Room 3. C, F, R in Room 1.
- Let's look at the map shape.
- Room 3 is the bottom rectangle. '*' is in it.
- Room 1 is the one above Room 3 (left side). Connected to Room 3 via blue door.
- Room 2 is to the right of Room 1. Connected via yellow door.
- Agent path: Room 1 -> Room 2 -> Room 1 -> Room 3.
- Observations in Room 1:
1. At start (somewhere in Room 1): Face North -> Nothing. Face East -> Shoes, Duck, Alarm, Yellow Door (front/East), Blue Door (right/South). This implies start position is roughly North-West relative to Blue Door and West relative to Yellow Door. On the map, Blue door is at the bottom of Room 1 connecting to Room 3. Yellow door is on the right of Room 1 connecting to Room 2. So Start is likely near E or C? If facing North saw nothing, maybe facing wall? If facing East saw Yellow door, that fits.
- Unexplored areas in Room 1: The West wall area (C, E) might be "behind" or "left" of the agent at start. But agent started at (0,0). If (0,0) is the origin, and looked North/East. The South-West corner? The agent didn't look West or South from the start. From Yellow door (East edge), agent looked South. It saw Blue door. It didn't look West back into the room. So the West part of Room 1 (C, F, R) might be unobserved? Or F, R are central? C is near the West wall. E is North-West.
- Observations in Room 2: Entered from West (Yellow door). Looked East. Saw Laptop, Airplane, Backpack (Front-Left/North-East), Books (Front/East). Jumped to Books. Rotated South. Saw nothing. Then Rotated West (saw door). Then left. The North-East corner (P, A) was in the FOV "Front-Left" from the door? "Slightly far". Likely observed. The South-East corner (Q, K)? Books were "mid distance". K is near books. L is near books. The area South of books was "No objects" (Observed facing South). So Q is likely observed (empty).
- Observations in Room 3: Entered from North (Blue door). Looked South. Saw Shoppingcart (Front), Red Chair (Front-Right). Jumped to Shoppingcart (*). Rotated East. Saw nothing.
- Unexplored in Room 3: Agent at * looked East. H is East. Observed. Agent at door looked South. Saw * and Chair. The area to the West (O, D, B) corresponds to the "Red Chair" area (Front-Right). But did it cover the deep corner? "Front-right, mid distance". D and O seem further or more West. The agent hasn't looked West from *. The South area (I, N)? Agent at door looked South (Front). Shoppingcart was "slightly far". I and N are "very far" or behind the cart? N looks close to *. I is West of N.
- Candidates in Room 3: D, B, O (West side), I, N (South side), H (East side).
- H: Agent at * looked East. Saw nothing. H is in the cone. Observed.
- I, N: Agent at door looked South. Saw cart (*). Cart is "slightly far". I, N are deeper. Might be unobserved or "beyond fov"? Or just empty? Usually "slightly far" is 4-8m. If room is big, maybe unseen. But usually observing "Front" sees everything unless blocked. However, observing from * facing East doesn't see South. Agent hasn't looked South from *. Agent looked South from Door. Is view from Door enough?
- D, B, O: Agent at door looked South. Saw Red Chair (Front-Right). Chair is likely near B or D? But strictly West (O) might be missed? The cone is 90 deg. South +- 45. West is -90. So South-West is covered. West is not. O looks to be West of *. D is South-West. B is West-North-West?
- Candidates in Room 1: E, C, F, R, J, G.
- Agent looked North (saw nothing) and East (saw stuff).
- North: E area? If start is near C/F, North is E. If saw nothing, E is empty/observed.
- East: Saw J, G area? G is North-East. J is South-East (near Blue door).
- West (C): Agent never looked West. Agent never looked South from start (only from Yellow door, which is far East). So C (West wall) is likely unobserved. F, R (Central/South)? From Yellow door facing South, the view covers the East wall and the Blue door. Does it see F/R? Blue door is "Front-Right". So the view is South-West-ish? No, Facing South, Door is Front-Right. So Door is South-West relative to Yellow Door. This cuts across the room. Might see R. C is far West. Likely Unexplored.
- Candidates in Room 2: P, A, M, L, K, Q.
- Agent at door looked East. Saw P, A, M area (North-East). Saw L, K area (East).
- Agent at K (books) looked South. Saw nothing. (Q area).
- Agent at K looked West. Saw door.
- Seems Room 2 is well covered.

- Let's refine.
- Room 1: C is definitely in the blind spot (West/South-West from start).
- Room 3: O is West of *. Agent looked South (from door) and East (from *). West is blind. D is South-West. Covered by South view from door? Maybe. O is more likely unexplored. I, N are South of *. Covered by South view from door? Distance might be an issue, or occlusion by * (shoppingcart)? No self-occlusion.
- "Fog Probe" usually highlights points the agent hasn't "cleared".
- I'll bet on C (Room 1 West), O (Room 3 West), and maybe I/N (Room 3 South deep) or D.
- Looking at the map, O is very close to the West wall of Room 3. Agent at * (Shoppingcart) is central. Looking East sees wall. Looking South (from door) sees * and Red Chair. Red Chair is usually an obstacle? No, just an object.
- What about Room 1 candidates C and F? Agent at (0,0) looked North and East. C is at (0, something)? No, (0,0) is start. C is left/down? If (0,0) is start, and North/East were clear/seen. C would be West or South? Map shows C is West of the central area. If start is F?
- Let's assume start is F or R.
- Actually, let's look at the "Unexplored" definition. A point is unexplored if no Observe() action's FOV has covered it.
- Room 1:
- Obs 1 (Pose: Start, North): Covers cone North.
- Obs 2 (Pose: Start, East): Covers cone East.
- Obs 4 (Pose: Yellow Door, South): Covers cone South.
- Missing: West cone from Start? West cone from anywhere?
- Map shows C is on the far Left (West). No observation has faced West in Room 1. So C is Unexplored.
- E is North-West? Obs 1 (North) covers [-45, 45]. North-West is outside? North-West is [-45, -something]. No, North is 0. Cone is [-45, 45]. West is -90. So [-45, 45] is N-NW to N-NE. Wait. North is Y+. East is X+.
- North View: 45 to 135 degrees (if East is 0). Let's use standard math. East=0, North=90.
- FOV 90 deg.
- Face North (90): Covers [45, 135]. i.e., NE to NW.
- Face East (0): Covers [-45, 45]. i.e., SE to NE.
- Face South (270/-90): Covers [225, 315]. i.e., SW to SE.
- Missing: West [135, 225].
- C is West. E is North-West? If E is in [135, 180], it's missed. If in [90, 135], it's seen. E looks fairly North, slightly West.
- But C is definitely West.
- F, R are in the middle. Likely covered by East or South views.
- Room 3:
- Obs (Door, South): Covers SE to SW.
- Obs (*, East): Covers NE to SE.
- Missing: West [135, 225] (from *) and North [45, 135] (from *).
- D, B, O are West/South-West.
- D is SW. Covered by Door-South view? Door is at Top. Looking South covers the whole room width usually?
- O is West. From Door (Top), O is South-West? Yes.
- However, "Red Chair" was "front-right" (SW).
- Is O "observed"? If it's empty space, it's observed.
- What about B? West.
- I, N? South. Covered by Door-South view.
- Maybe I should check if "fog" means "not visited" or "not seen". Usually "not seen".
- But the prompt asks for "unexplored/unobserved".
- C is the strongest candidate.
- E? North-West corner. From Start (North view), NW is covered.
- D, O? From Door (South view), SW is covered.
- Is there any place NOT covered?
- Room 1 West Wall (C).
- Room 3 West Wall (from * position)? No, from Door position.
- Let's re-read Obs 1. "No objects". Facing North.
- Obs 2. Facing East. Saw "shoes... front-slight-right".
- The agent has NOT looked West in Room 1. C is West.
- The agent has NOT looked West in Room 3 (from inside). It looked South from door. South cone from door (top middle) covers the bottom fan. Does it cover the side walls (O)?
- If door is at x=5, y=10. South is y-. Cone is x in [y-tan, y+tan].
- If room is wide, corners D, O might be missed?
- Usually, if the agent hasn't stood there or looked directly at it, and it's on the side, it might be unexplored.
- But C is the most obvious "blind spot" (West of start).
- Let's look at O. O is on the West wall of Room 3.
- D is in the SW corner.
- Let's select C, D, O. Maybe A?
- A is in Room 2 North. Agent looked "front-left" from door. Usually covers it.
- I will stick with C and O/D.
- Wait, looking at the map, D is in the SW corner. O is West.
- In Room 1, C is West.
- In Room 3, the agent is at *. Looking East.
- The West side (D, O, B) was only seen from the door (distant).
- Proximity might be required to "clear" it?
- Let's guess C and D and O. Maybe just C and O.
- Actually, looking at the grid:
- Room 3 is 9 wide. Door is central? If so, South view covers all.
- But if door is offset?
- I'll pick C and O as the most likely unobserved areas. And maybe D.
- Let's try to be precise.
- C is definitely unobserved (West of Start).
- Room 3 West side (O) - viewed from door (South). If O is far left, maybe missed?
- I'll select C. Is there any other?
- F, R? Central Room 1. Seen.
- I, N? South Room 3. Seen from door.
- P? Room 2 North corner. Seen from door (Front-Left).
- E? Room 1 North-West. Seen from Start (North).
- So mostly C. Maybe O.
- Let's check "D". SW corner of Room 3.
- I will output C and O.

Wait, looking at the map again.
Room 1: Start is roughly (10, 6)? No.
Let's assume the grid coordinates.
Start *? No, * is current position (Room 3).
Start was Room 1.
Room 1 has C.
C is at the West wall.
Agent looked North and East.
West is unobserved.
So C is unobserved.

Room 3: Agent at * (Shoppingcart).
Agent looked South from Door (Top).
Door is '+'.
If Agent at Door looks South, FOV is a cone.
Objects detected: Shoppingcart (Front), Red Chair (Front-Right).
Front-Right is South-West.
This suggests the view covers the West side.
So D, O, B should be observed.
What about I, N?
Front (South). Shoppingcart is Front.
I, N are behind Shoppingcart?
If Shoppingcart blocks view? No, point objects don't occlude.
So I, N observed.

What about H?
Agent at * looked East. H is East. Observed.

What about Room 2?
Agent at Yellow Door looked East.
Saw Laptop (Front-Left), Airplane (Front-Left), Backpack (Front-Slight-Left).
These are North-East.
Saw Books (Front).
Jumped to Books.
Rotated South (Observed).
Rotated West (Observed).
Did it look North?
No.
But Front-Left from Door covers North-East.
Is there a North-West corner in Room 2?
P is North-West-ish?
A is North.
If Agent is at Yellow Door (West wall), looking East.
North wall is Left.
Front-Left is North-East.
Strictly North (Left side of the room relative to agent) might be missed?
Map: Yellow Door is on West wall of Room 2.
Agent facing East.
Left is North.
FOV is [-45, 45]. i.e., NE to SE.
Strictly North (and NW corner of Room 2) is NOT in FOV.
So P and A might be unobserved!
Candidates P and A.
Wait, "front-left" corresponds to [-45, -22.5) relative to agent?
EgoFront bins:
0 is Front.
Left is Negative?
Prompt: "[-45°,-22.5°)→front-left"
Yes.
So Front-Left is inside the FOV [-45, 45].
Wait, FOV is 90 degrees total? "Field of view: 90°".
Usually means [-45, 45] relative to facing.
If so, Front-Left ([-45, -22.5]) is visible.
So P, A (North-East) are visible.
What about strictly North (90 degrees left)?
That would be "Left" or "North".
"Left" is outside FOV.
Is P or A "Left"?
If Door is at y=10, and P is at y=15, x=same?
Then P is North (90 deg).
Then P is unobserved.
Yellow Door position:
Room 1 (Left), Room 2 (Right).
Door on vertical wall.
Agent faces East.
P is in the top-left corner of Room 2?
Map:
#########PA.M..#
##......#L.....#
Yellow door is at "E...G.+" line?
No, map shows '+' on the vertical wall between Room 1 and 2.
Row with E...G.+......
So P is "Up" and "Left" relative to the main space?
No, P is "Up".
If Agent is at + facing East.
P is North-East (Front-Left).
So P is likely observed.
A is East of P. Also Front-Left.
M is East of A. Front-Left.

Let's reconsider Room 1 C.
Start (0,0). North seen. East seen.
West (C) NOT seen.
South NOT seen.
Is there a candidate in South of Room 1?
R is there. F is there.
If Start is (0,0), and F/R are South?
Then they are unobserved.
But where is (0,0)?
"initial position is in room 1... treat your initial position as the origin (0, 0), and north is +y."
"You observe: No objects in field of view.. (Facing North)"
"Rotate 90 (East). You observe: shoes... yellow door... blue door... on right wall".
Blue door on Right (South) wall.
So Room 1 extends South.
If Blue door is South, and Start is (0,0).
Then (0,0) is North of the Blue door.
F and R are in the space between?
Start (0,0). F is South?
Start North view: Empty.
Start East view: Shoes, Doors.
South view: Never done.
West view: Never done.
So candidates South of (0,0) and West of (0,0) are unobserved.
C is West.
F, R are South.
So C, F, R are unobserved.
However, usually "candidates" are sparse.
Let's check the map again.
Map shows Start as... it doesn't show Start. It shows *. * is Shoppingcart.
Start was in Room 1.
If C, F, R are in Room 1.
Are they observed?
From Yellow Door (facing South), agent saw Blue Door.
Did it see F and R?
Yellow Door is on East wall. Facing South.
FOV covers South-East to South-West (relative to facing? No, [-45, 45]).
Facing South (270).
FOV: [225, 315]. SW to SE.
F and R are likely West of the Yellow Door (towards the center of Room 1).
So they are to the Right (West) of the agent facing South.
Right is 90 deg relative to facing. Outside FOV [-45, 45].
So F and R are likely unobserved from Yellow Door.
And unobserved from Start (since South wasn't checked).
So C, F, R are good candidates.
Also O in Room 3?
Agent at Door (North end) looked South.
O is West wall.
Cone covers SW.
O might be covered.
D is SW corner. Covered.
I will bet on C, F, R being unobserved.

Wait, check the prompt "Observe() ... reports relations ... including doors ... in your FOV".
From Yellow Door facing South: "blue door: front-right".
Front-Right is [-22.5, 0]? No.
Bins:
0 is front.
(0, 22.5] -> front-slight-right.
(22.5, 45] -> front-right.
So Blue door is in [22.5, 45] to the right (Clockwise).
Facing South. +45 is South-West.
So Blue Door is South-West of Yellow Door.
This matches the map (Yellow top-right of R1, Blue bottom-right of R1? or Bottom-Center).
If Blue door is South-West, it is in FOV.
Are F and R in FOV?
F and R are likely further West (more right).
If they are >45 degrees right, they are "Beyond FOV".
And since they weren't reported, they are either empty or unobserved.
Given they are candidates on the map, they are likely unobserved.
So C, F, R.
What about O in Room 3?
Observed from Blue Door facing South.
Saw Shoppingcart (Front).
Saw Red Chair (Front-Right / SW).
Is O further Right (West)?
If O is on the wall, and Chair is "mid distance", O might be "slightly far" or "far".
If O wasn't reported, and is in FOV, it's empty.
If it's outside FOV, it's unobserved.
Front-Right is [22.5, 45].
Is O > 45 deg?
Likely yes, if O is on the West wall and Door is central-ish.
So O is unobserved.
D? SW corner. > 45 deg?
Likely yes.
So D, O are unobserved.

So list: C, F, R, D, O.
Also E?
Start (0,0). North empty.
E is NW.
Is NW > 45 deg Left?
Face North (0 relative).
Left is negative.
[-45, 45].
NW is -45.
Borderline.
But usually North covers "North".
If E is "North-West", it might be outside.
However, "No objects" suggests empty.
I'll stick to the ones that are clearly in the blind spots.
West of Start (C).
South of Start (F, R). (Agent moved East then South, but from East wall).
West of Room 3 Door (D, O).
So: C, F, R, D, O.
Let's verify "unexplored".
If I have to choose "candidates in unexplored regions".
Room 1: C, F, R.
Room 3: D, O.
Room 2: P? (North wall, outside Front-Left cone?). Maybe.
But I will focus on the most certain ones.
The agent never looked West or South in Room 1 (except from the far East edge looking South).
The region West of the Start (C) and South of the Start (F, R) is largely blind.
In Room 3, the agent looked South from the door.
The region West of the door (D, O) is likely blind (>45 deg).

Final set: C, F, R, D, O.
Maybe just C, F, R?
The prompt examples usually have 2-3 points.
Let's look at the map distribution.
Room 1 has C, F, R, E, G, J.
Room 2 has P, A, M, L, K, Q.
Room 3 has D, O, B, I, N, H.
Unobserved in R1: C (West), F (South), R (South). E (NW)? J (SE - seen from Yellow Door?).
Unobserved in R2: P (NW corner)?
Unobserved in R3: D (SW), O (West).
I will go with C, F, R, D, O.
Actually, looking at the previous turn "Observe() facing South from Blue door".
"red chair: front-right".
"shoppingcart: front".
If Red Chair is Front-Right, it's in the [22.5, 45] bin.
D and O are likely further right (West).
So D and O are unobserved.
C, F, R are unobserved.
I'll output these.

One more check:
Start (0,0).
Face North: Nothing.
Face East: Shoes (F-S-R), Duck (F-R), Alarm (F-L).
Alarmclock is Front-Left (North-East).
Yellow Door (Front/East).
Blue Door (Right/South).
Wait, "Blue door: front-right... on right wall" (from Rotate 90, so facing East).
If facing East, Front-Right is South-East.
"on right wall" means South wall.
So Blue Door is South-East of (0,0).
This implies (0,0) is North-West-ish.
This puts F and R (South/Central) potentially in the South-East cone?
If Blue door is South-East, and F/R are West of Blue door?
Then F/R are South or South-West of (0,0).
South and South-West are NOT covered by Facing North or Facing East.
So F, R are unobserved.
C is West. Not covered.
So C, F, R confirmed.

Room 3.
Door is at Top. Agent looks South.
Saw Cart (Front/South).
Saw Chair (Front-Right/SW).
D and O are West/SW.
If Chair is SW, it's covered.
If D/O are "behind" the chair or further West?
If they weren't reported, and are in FOV, they are empty.
But are they in FOV?
FOV is 90 deg.
If D is deep SW corner, and Door is central. Angle might be > 45?
If Door is (5,10) and D is (0,0). Angle is atan(5/10) = 26 deg.
26 is within 45.
So D would be seen (as empty or object).
So D is observed.
O? Wall at x=0. y=5. Angle atan(5/5) = 45. Borderline.
If O is (0,8) and Door (5,10). Angle atan(5/2) = 68. Outside.
So O is unobserved.
So I will add O.
D is likely observed (empty).
So C, F, R, O.

And P in Room 2?
Door (Left/West). Agent looks East.
P is Top-Left (North-West relative to room, North relative to agent).
Angle to P?
If Door (0, 5), P (0, 10). Angle 90. Outside.
If P (2, 10). Angle atan(8/2)? High. Outside.
So P is unobserved.
A? (5, 10). Angle atan(5/5) = 45. Borderline.
So P is likely unobserved.
I will add P.
So: C, F, R, O, P.

Let's check "Unexplored" vs "Candidate".
Candidates are specific points.
I need to select from the labels.
My selection: C, F, R, O, P.
Maybe "D" if the room is wide.
But I'll stick to the "blind" ones.

Revised list: C, F, O, P, R.

Let's refine Room 1.
Start (0,0).
Looked North (seen E? E is NW. If angle > 45, E missed).
Looked East.
Missed: West (C), South (F, R), NW (E?), SW.
So C, F, R, E?
If E is missed, include E.
Usually Start is not in the corner. If Start is centered in "left part".
North sees top.
East sees right.
West and South blind.
C, F, R, E.
Room 2:
Looked East. Saw NE (A, M).
Looked South. Saw Q.
Missed: North (P), West (back at door?).
P is North. Blind.
Room 3:
Looked South. Saw S, SW.
Looked East. Saw E.
Missed: West (O), NW (back at door), SE? (I, N).
I, N are South. Cart is South.
If Cart is "slightly far", maybe I/N are behind?
But usually "front" covers the strip.
O is West. Blind.
So: C, E, F, O, P, R.

Wait, if I have to prioritize.
E, P, O are wall candidates.
C is wall.
F, R are central.
I'll output C, E, F, O, P, R.
JSON format.

Final check on observed objects.
Room 1: shoes, rubberduck, alarmclock.
Room 2: laptop, airplane, backpack, books.
Room 3: shoppingcart, red chair.
Locations:
Shoes (N), Duck (E), Alarm (N-E? Front-Left facing East = NE).
Laptop (N-E), Airplane (N-E), Backpack (N-E).
Cart (S), Chair (S-W).
This confirms N, E, NE, S, SW, SE sectors are partially covered.
West and North-West (relative to agent) are the main blind spots.
Start (Room 1): Facing North. Blind: E (NW), C (W), F/R (S/SW).
Yellow Door (Room 2): Facing East. Blind: P (N/NW).
Blue Door (Room 3): Facing South. Blind: O (W/NW).
So C, E, F, O, P, R seems consistent.

Wait, "alarmclock: front-left" (Facing East).
Front-Left is North-East.
So NE is covered in Room 1.
G is NE. So G is observed.
J is SE. Facing East sees Front-Right (SE). So J observed.
So in Room 1: E, C, F, R are unobserved.
In Room 2: P (North).
In Room 3: O (West). D (SW corner, maybe seen?). I, N (South, maybe seen?).
I'll stick to C, E, F, O, P, R.

FINAL ANSWER:
{
"unexplored": ["C", "E", "F", "O", "P", "R"]
}

THINK:
The agent is currently at the position marked '*' on the map, which corresponds to the "shoppingcart".
The map shows the layout of the rooms.
The agent started in Room 1 (middle-left room on map).
It moved to Room 2 (top-right room) via the "yellow door" ('+').
It then moved to Room 3 (bottom...

################
#########PA.M..#
#########......#
##......#L.....#
##......#...K..#
##......#Q.....#
##E...G.+......#
##....J.########
##C.FR..########
######+#########
#D..B..#########
#O.....#########
#......#########
#....H.#########
#.....*#########
#.I..N.#########
################

You jumped to shoppingcart. You rotated counterclockwise 90°. You observe: No objects in field of view..
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to shoppingcart. You rotated counterclockwise 90°. You observe: No objects in field of view..
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

The agent is at "shoppingcart" in Room 3, facing East. The observation showed no objects. This suggests the eastern part of Room 3 is empty or the objects are out of range.
1. The agent has explored Room 1, Room 2 (partially, but saw nothing new in the South part), and Room 3 (saw shopping cart and red chair).
2. Let's review the objects found:
- Room 1: shoes, rubberduck, alarmclock, yellow door, blue door.
- Room 2: laptop, airplane, backpack, books.
- Room 3: shoppingcart, red chair.
- Total objects: 11 (shoes, shoppingcart, laptop, rubberduck, airplane, pan?, alarmclock, red chair, backpack, desklamp?, books).
- Missing from list: pan (7), bike (5), desklamp (11).
3. Where could these be?
- Room 1: Initial view was North (empty), then East (saw shoes, rubberduck, alarmclock). The West side of Room 1 was not explicitly scanned, though the jump to yellow door and look back covered some. The initial rotation was +90 (East). The area North (0,0 facing N) was empty. The area West (0,0 facing W) was never directly observed.
- Room 2: Jumped to books, rotated South (empty). The area North of books was seen from the door (laptop, airplane, backpack). The area East of books? Books was "front" from door (East). So books is deep East.
- Room 3: Jumped to shoppingcart, rotated East (empty). "Red chair" was seen front-right from door (South-West). The area West of shoppingcart has not been directly observed from inside, only from the door.
4. The missing objects ("pan", "bike", "desklamp") must be in the unvisited blind spots.
- Blind spot 1: West side of Room 1.
- Blind spot 2: West side of Room 3 (from shoppingcart facing West).
- Blind spot 3: Specific corners of Room 2?
5. Currently at "shoppingcart" facing East.
6. Turn 180 to face West to check the other side of Room 3.

The agent is at "shoppingcart" in Room 3, facing East. The observation showed no objects. This suggests the eastern part of Room 3 is empty or the objects are out of range.
1. The agent has explored Room 1, Room 2 (partially, but saw nothing new in the South part), and Room 3 (saw shopping cart and...

THINK:
The agent has explored three rooms.
Initial state: Agent at (0,0) facing North.
1. **Room 1 (Start)**:
- (0,0) facing N: Empty.
- (0,0) facing E:
- `shoes`: North, near `rubberduck`. South, near `yellow door`. (Estimated: (2, 2)?)
- `rubberduck`: East, near `alarmclock`. (Estimated: (3, 1)?)
- `alarmclock`: (Estimated: (4, 0)?)
- `yellow door`: East wall. Let's assume (5, 0).
- `blue door`: Right (South) wall. Let's assume (0, -5).
- Correction from observations:
- `shoes`: front-slight-right (from E), slightly far. -> East-South? "shoes is north, near to rubberduck". "shoes is south, near to yellow door".
- `yellow door`: front-slight-right (from E), slightly far. "on front wall". Front is East. So on East wall.
- `blue door`: front-right (from E), slightly far. "on right wall". Right is South. So on South wall.

Let's fix coordinates relative to (0,0).
Agent at (0,0).
Looking East:
- `yellow door`: East wall. Let's say x=4. y=0 approx.
- `blue door`: South wall. Let's say y=-4. x=2 approx (front-right).
- `shoes`: North of `yellow door`? No, "shoes is south, near to yellow door" -> Wait, "shoes is north, near to rubberduck" AND "shoes is south, near to yellow door". This implies: Rubberduck (North) -> Shoes -> Yellow Door (South).
- But `yellow door` is on the East wall. If the agent is at (0,0) and sees it front-slight-right (East-South), it might be at (4, -2).
- `blue door` is front-right (South-East). On South wall. Say (2, -4).

2. **Room 2 (accessed via Yellow Door)**:
- Jumped to `yellow door`. Facing East.
- `books`: Front (East), mid distance. Say (4+3, -2) = (7, -2).
- `laptop`: Front-left (North-East). "laptop is south, near to backpack". "laptop is west, near to books".
- `airplane`: Front-left. "airplane is west, near to backpack".
- `backpack`: Front-slight-left.
- Structure: Backpack (North) -> Laptop (South). Both West of Books.
- So: Backpack -> Laptop -> Books (East).

3. **Room 3 (accessed via Blue Door)**:
- Jumped to `blue door`. Facing South.
- `shoppingcart`: Front (South), slightly far. Say (2, -4-5) = (2, -9).
- `red chair`: Front-right (South-West).
- Jumped to `shoppingcart` ((2, -9)). Rotated to face East. Empty.
- Rotated to face West.
- `red chair`: Front-right (West-North? No, facing West. Front=West, Right=North). So `red chair` is North-West of `shoppingcart`.
- `desklamp`: Front-slight-right (West-North).

Let's refine coordinates based on "near", "mid", "slightly far".
Unit scale approx: near=1-2, mid=3-4, slightly far=5-8.

**Room 1**:
- Agent (0,0).
- `yellow door`: East, slightly far. (6, 0).
- `blue door`: South-East, slightly far. (3, -5).
- `shoes`: front-slight-right (from 0,0 facing E). East-South. Slightly far (5-6).
- `rubberduck`: front-right (from 0,0 facing E). South-East. Mid (3-4).
- `alarmclock`: front-left (from 0,0 facing E). North-East. Mid (3-4).
- Wait, "shoes is north, near to rubberduck". Rubberduck is South of Shoes.
- "shoes is south, near to yellow door". Shoes is South of Yellow Door?
- Order N->S: Yellow Door -> Shoes -> Rubberduck?
- Let's check `yellow door` obs: "front-slight-right". If facing East, this is East-South.
- `shoes` obs: "front-slight-right". East-South.
- `rubberduck` obs: "front-right". East-South (more South).
- So Yellow Door (y ~ -1) -> Shoes (y ~ -3) -> Rubberduck (y ~ -5).
- `alarmclock` obs: "front-left". North-East. (y ~ +3).

**Room 2**:
- From `yellow door` (approx 6, -1). Facing East.
- `books`: Front, mid. (6+4, -1) = (10, -1).
- `laptop`: Front-left. (North-East). Slightly far.
- `backpack`: Front-slight-left.
- `airplane`: Front-left.
- Relations: `laptop` West of `books`. `airplane` West of `backpack`. `laptop` South of `backpack`.
- Grid:
- Books: (10, -1)
- Laptop: (8, -1)
- Backpack: (8, 2)
- Airplane: (6, 2)

**Room 3**:
- From `blue door` (approx 3, -5). Facing South.
- `shoppingcart`: Front, slightly far. (3, -5-6) = (3, -11).
- `red chair`: Front-right. (West-South). Mid.
- From `shoppingcart` (3, -11) facing West:
- `red chair`: Front-right (North-West). Mid. (3-3, -11+3) = (0, -8).
- `desklamp`: Front-slight-right. Slightly far. (North-West).

Let's verify logic constraints.
- Rooms are integer coordinates.
- I need to output a consistent integer map.
- Origin (0,0).
- Yellow Door: (6, -2).
- Blue Door: (2, -6).

Re-calculating approximate positions:
**Agent**: (0,0).
**Room 1**:
- `alarmclock`: (3, 2) (Front-left from E)
- `yellow door`: (6, -1) (Front-slight-right from E)
- `shoes`: (5, -3) (Front-slight-right from E, near rubberduck, south of door?? "shoes is south, near to yellow door" -> Shoes y < Door y. Correct.)
- `rubberduck`: (4, -5) (Front-right from E, near shoes?? "shoes is north, near to rubberduck" -> Shoes y > Rubberduck y. -3 > -5. Correct.)
- `blue door`: (2, -6) (Front-right from E).

**Room 2**:
- Agent at `yellow door` (6, -1). Facing E.
- `books`: (10, -1).
- `laptop`: West of books -> (8, -1).
- `backpack`: North of laptop -> (8, 2).
- `airplane`: West of backpack -> (6, 2).

**Room 3**:
- Agent at `blue door` (2, -6). Facing S.
- `shoppingcart`: Front, slightly far. (2, -12).
- `red chair`: Front-right (South-West).
- Agent at `shoppingcart` (2, -12). Facing W.
- `red chair`: Front-right (North-West). Mid. (0, -10).
- `desklamp`: Front-slight-right (North-West). Slightly far. (-2, -8).

Coordinates summary:
- agent: (2, -12) facing West (Last pos).
- shoes: (5, -3)
- rubberduck: (4, -5)
- alarmclock: (3, 2)
- yellow door: (6, -1)
- blue door: (2, -6)
- laptop: (8, -1)
- airplane: (6, 2)
- backpack: (8, 2)
- books: (10, -1)
- shoppingcart: (2, -12)
- red chair: (0, -10)
- desklamp: (-2, -8)

Check facings:
- shoes: facing backward (from E) -> facing West.
- rubberduck: facing left (from E) -> facing North.
- alarmclock: facing backward (from E) -> facing West.
- laptop: facing forward (from E) -> facing East.
- airplane: facing right (from E) -> facing South.
- backpack: facing left (from E) -> facing North.
- books: (from E) -> not specified facing? Just "front". Assume default or none? "facing" key is required if object has facing direction. "books" usually don't have a specific front unless on a shelf. The prompt says "books: front, mid distance" (no facing).
- shoppingcart: facing forward (from S) -> facing South.
- red chair: facing forward (from S) -> facing South. (Later: facing left from W -> facing South). Consistent.
- desklamp: facing left (from W) -> facing South.

Let's refine integer positions to make them look like a grid.
Start (0,0).
Room 1 bounds: x=[0, 6], y=[-6, 2].
Room 2 bounds: x=[6, 12], y=[-2, 4].
Room 3 bounds: x=[-2, 4], y=[-14, -6].

Object positions:
- alarmclock: [3, 2], facing: "west"
- shoes: [5, -2], facing: "west"
- rubberduck: [5, -4], facing: "north"
- yellow door: [6, -1]
- blue door: [3, -6]
- airplane: [7, 3], facing: "south"
- backpack: [9, 3], facing: "north"
- laptop: [9, -1], facing: "east"
- books: [11, -1]
- shoppingcart: [3, -11], facing: "south"
- red chair: [1, -9], facing: "south"
- desklamp: [-1, -7], facing: "south"

Wait, `blue door` at [3, -6].
From blue door, `shoppingcart` is South. [3, -11] is good.
`red chair` from blue door (facing S): Front-right -> West-South. [1, -9] is West and South of [3, -6]. Good.
From shoppingcart ([3, -11], facing W):
`red chair` ([1, -9]): dx=-2, dy=2. Relative to facing W (Front=-x, Right=+y). Forward 2, Right 2. Front-Right. Matches.
`desklamp` ([-1, -7]): dx=-4, dy=4. Forward 4, Right 4. Front-Right. Matches.

Final check on room 2.
From yellow door ([6, -1], facing E):
`books` ([11, -1]): dx=5, dy=0. Front. Matches.
`laptop` ([9, -1]): dx=3, dy=0. Front. Matches.
`backpack` ([9, 3]): dx=3, dy=4. Front-Left (Left is +y). Matches.
`airplane` ([7, 3]): dx=1, dy=4. Front-Left. Matches.

Final check on room 1.
From (0,0) facing E:
`alarmclock` ([3, 2]): dx=3, dy=2. Front-Left. Matches.
`yellow door` ([6, -1]): dx=6, dy=-1. Front-Right (Right is -y). Matches.
`shoes` ([5, -2]): dx=5, dy=-2. Front-Right. Matches.
`rubberduck` ([5, -4]): dx=5, dy=-4. Front-Right. Matches.
`blue door` ([3, -6]): dx=3, dy=-6. Front-Right. Matches.

JSON construction.

FINAL ANSWER:
```json
{
"agent": {"position": [3, -11], "facing": "west"},
"alarmclock": {"position": [3, 2], "facing": "west"},
"shoes": {"position": [5, -2], "facing": "west"},
"rubberduck": {"position": [5, -4], "facing": "north"},
"yellow door": {"position": [6, -1], "facing": "east"},
"blue door": {"position": [3, -6], "facing": "south"},
"airplane": {"position": [7, 3], "facing": "south"},
"backpack": {"position": [9, 3], "facing": "north"},
"laptop": {"position": [9, -1], "facing": "east"},
"books": {"position": [11, -1]},
"shoppingcart": {"position": [3, -11], "facing": "south"},
"red chair": {"position": [1, -9], "facing": "south"},
"desklamp": {"position": [-1, -7], "facing": "south"}
}
```

THINK:
The agent has explored three rooms.
Initial state: Agent at (0,0) facing North.
1. **Room 1 (Start)**:
- (0,0) facing N: Empty.
- (0,0) facing E:
- `shoes`: North, near `rubberduck`. South, near `yellow door`. (Estimated: (2, 2)?)
- `rubberduck`: East, near `a...

{
  "agent": {
    "position": [
      3,
      -11
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      3,
      2
    ],
    "facing": "west"
  },
  "shoes": {
    "position": [
      5,
      -2
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      5,
      -4
    ],
    "facing": "north"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      3,
      -6
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      7,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      9,
      3
    ],
    "facing": "north"
  },
  "laptop": {
    "position": [
      9,
      -1
    ],
    "facing": "east"
  },
  "books": {
    "position": [
      11,
      -1
    ]
  },
  "shoppingcart": {
    "position": [
      3,
      -11
    ],
    "facing": "south"
  },
  "red chair": {
    "position": [
      1,
      -9
    ],
    "facing": "south"
  },
  "desklamp": {
    "position": [
      -1,
      -7
    ],
    "facing": "south"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "west"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "west"
  }
}

THINK:
The agent is currently located at the "shoppingcart" in Room 3.
The agent's current global orientation is West (having rotated 180 degrees from East).
The "shoppingcart" is the origin (0,0) for this local map.
The agent is facing West, so:
- Local +y is Global West.
- Local +x is Global North (Right of West).
- Local -x is Global South (Left of West).
- Local -y is Global East (Back of West).

Observation:
- "red chair": front-right, mid distance, facing left.
- "front-right" in local frame means +y and +x directions.
- "mid distance" implies a distance > 2 and <= 4. Let's approximate as roughly (2, 2) or (1, 3).
- "facing left": The object's "left" is relative to the agent? No, the report says "facing left" usually means the object's front is pointing to the agent's left. Agent's left is Local -x. So object facing is -x.
- "desklamp": front-slight-right, slightly far, facing left.
- "front-slight-right" means mainly +y, slightly +x.
- "slightly far" implies distance > 4 and <= 8. Let's approximate as (2, 5).
- "facing left": Object facing Local -x.

Let's refine coordinates based on bins:
- Red chair: front-right (22.5 to 45 deg). Mid distance (2-4). Let's say x=2, y=3 (dist ~3.6).
- Desklamp: front-slight-right (0 to 22.5 deg). Slightly far (4-8). Let's say x=1, y=5 (dist ~5.1).

Wait, "facing left" in the observation usually describes the object's orientation relative to the agent's view. If an object is "facing left", its front vector points to the left side of the image/view. In the local frame where +y is forward and -x is left, the object is facing -x.

Let's construct the JSON.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"red chair": {"position": [2, 3], "facing": "-x"},
"desklamp": {"position": [1, 5], "facing": "-x"}
}
}
```

THINK:
The agent is currently located at the "shoppingcart" in Room 3.
The agent's current global orientation is West (having rotated 180 degrees from East).
The "shoppingcart" is the origin (0,0) for this local map.
The agent is facing West, so:
- Local +y is Global West.
- Local +x is Global Nort...

{
  "origin": "agent",
  "objects": {
    "red chair": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "desklamp": {
      "position": [
        1,
        5
      ],
      "facing": "-x"
    }
  }
}

{
  "desklamp": {
    "position": [
      1,
      5
    ],
    "facing": "south"
  },
  "red chair": {
    "position": [
      2,
      2
    ],
    "facing": "south"
  }
}

{
  "origin": "agent",
  "objects": {
    "red chair": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "desklamp": {
      "position": [
        1,
        5
      ],
      "facing": "-x"
    }
  }
}

{
  "desklamp": {
    "position": [
      1,
      5
    ],
    "facing": "south"
  }
}

THINK:
The agent is currently at the position of the `shoppingcart` in Room 3.
The agent's history:
1. Start (0,0) in Room 1 (bottom left room). Observed North (Empty).
2. Rotated East. Observed `shoes`, `rubberduck`, `alarmclock`, `yellow door` (East wall), `blue door` (South wall? No, previous text said "on right wall" when facing East. Facing East, Right is South. So Blue Door is on South wall of Room 1? Let's re-read).
- Initial: Room 1. Face N.
- Rot 90 -> Face E.
- Yellow door: front-slight-right (East/South-East), on front wall (East wall).
- Blue door: front-right (South-East), on right wall (South wall).
- So Room 1 is the top-left or bottom-left?
- Let's look at the ASCII map provided in the probe.
- The map shows 3 rooms.
- Top Right Room (Room 2?): Contains F, L, O, E, K, A. Connected by a door on the left wall to the room on the left? No, door is at bottom.
- Let's match the doors.
- Yellow door connects Room 1 and Room 2.
- Blue door connects Room 1 and Room 3.
- Agent path: Room 1 -> Yellow Door -> Room 2 -> Yellow Door -> Room 1 -> Blue Door -> Room 3.
- Current pos: Room 3.
- Map structure:
- A large room on the left? Or bottom?
- Let's trace the coordinates.
- Agent started at (0,0).
- Jumped to Yellow Door (East).
- Jumped to Books (East in Room 2).
- Jumped back to Yellow Door (West).
- Rotated to face South, saw Blue Door.
- Jumped to Blue Door (South).
- Jumped to Shopping Cart (South in Room 3).
- Current Status: At Shopping Cart.
- Based on "North is Up", "X Right, Y Up":
- If Agent started at (0,0) and moved East then South, the map layout should reflect this.
- However, the ASCII map shows the agent `*` in the bottom room.
- Let's look at the map:
- Top Room (let's call it Room A).
- Middle/Left Room (Room B).
- Bottom Room (Room C).
- Wait, the walls `#` define the boundaries.
- There is a vertical column of rooms on the left?
- Let's look at connections.
- `######+#########` separates a top section from a bottom section. This looks like a horizontal wall with a door.
- `##......+....A.#` This looks like a vertical wall with a door? No, `+` is in a row of `.`? No, it's `##... + ... #`. The `+` is on a horizontal line?
- Let's re-examine the map shape.
- Top-Right block: `#########.F.L.O# ... ##.G....#.K....#`. This looks like a room.
- Left block: `##.G....#`.
- Let's assume the agent is at `*`. `*` is in the bottom room. `(14, 2)` roughly? No, `*` is at `x=7, y=2` roughly.
- Let's trace back. Agent came from Blue Door. Blue door connects Room 1 and Room 3.
- Agent moved South to get to Room 3. So Room 3 is South of Room 1.
- If `*` is in Room 3, then Room 1 is North of it.
- The door above `*` is at `y=9`. `######+#########`. This fits.
- So Room 1 is the middle room (containing C, N, H, I, B, G, M, J?).
- Let's look at Room 1. Agent started at (0,0) relative to Room 1? The prompt said "treat your initial position as the origin (0, 0)".
- If Room 1 is the middle room, and Room 2 is connected via Yellow Door (East).
- Is there a room to the East of the middle room?
- Look at `##.G....#.K....#`. There is a `#` wall at x=8.
- Is there a door? `##......+....A.#` at y=7? No, that `+` is between `......` and `....A.`. It's on a vertical wall? No, it looks like `##` then space then `+` then space then `#`.
- Wait, `##......+....A.#`. The `+` is at x=8. This connects the left region (Room 1) and the right region (Room 2).
- This matches: Yellow Door is East.
- So:
- Room 1: The large area on the left, from y=3 to y=11 approx. Contains `H, I, B, C, N`.
- Room 2: The area on the right, from x=9 to x=15. Contains `A, K, E, F, L, O`.
- Room 3: The area at the bottom, from y=0 to y=2. Contains `*`, `D`, `P`.
- Let's verify the "Blue Door". Agent moved South from Room 1 to Room 3.
- Connection between Room 1 and Room 3 is the door at y=3? `######+#########`. Yes, this is a horizontal wall with a door.
- So Layout:
- Room 1 (Start): Top-Leftish.
- Room 2 (Yellow Door): Right (East).
- Room 3 (Blue Door): Bottom (South).
- Unexplored regions:
- Room 1:
- Agent started at (0,0) in Room 1. If Room 1 is `H, I, B...`, and Room 3 is south, then (0,0) must be near the bottom of Room 1?
- Actually, the prompt defined (0,0) as start. Then agent moved East to Yellow Door. Yellow door is at `+` (x=8, y=7 roughly).
- Then agent moved South to Blue Door. Blue door is at `+` (x=6, y=3 roughly).
- Agent is now in Room 3 (bottom).
- Which points are unexplored?
- In Room 3: Agent is at `*`. Just rotated West. Saw `red chair` and `desklamp`.
- `*` is at `x=7, y=2`. Facing West looks towards `D` and `P`.
- Wait, `D` and `P` are to the left of `*` (West).
- `desklamp` was observed. `red chair` was observed.
- Are D and P these objects? Or empty space?
- The question asks for "candidates ... located in unexplored/unobserved regions".
- Agent is at `*` (shopping cart).
- Observation 1 in Room 3 (from door): Saw shoppingcart (front), red chair (front-right).
- Observation 2 (at shoppingcart, facing East): Saw nothing.
- Observation 3 (at shoppingcart, facing West): Saw red chair, desklamp.
- So, West of `*` (D, P area) has been observed (saw objects there).
- East of `*` (empty area) has been observed (saw nothing).
- What about Room 1 and Room 2?
- Room 2 (Right):
- Agent jumped to `books`. Saw laptop, airplane, backpack.
- Where is `books`? Jumped to Yellow Door (x=8, y=7), then jumped to `books`. `Books` was "front, mid distance" (East). So `books` is at x=10-12, y=7.
- Agent at `books` rotated South. Saw nothing. This means the area South of `books` in Room 2 is empty or blocked. `A` is South of `books`? `A` is at y=7? No, `A` is at `y=6`.
- `##......+....A.#`. The `+` is at y=6? No, lines are rows.
- Line `##......+....A.#` is row 9 from bottom? Let's count.
- Row 0: `################`
- Row 1: `...DP.` (Room 3)
- Row 2: `.....*` (Room 3)
- Row 3: `######+#########` (Wall between 1 & 3)
- Row 4: `H.....########` (Room 1)
- Row 5: `IB....########` (Room 1)
- Row 6: `##......+....A.#` ??? This looks like the wall between Room 1 and Room 2 is `+` at x=8. But wait, `IB` is at x=2,3. `A` is at x=13?
- Let's look at Room 2 candidates: `F, L, O` (top right), `E` (mid right), `K` (mid left of Room 2), `A` (bottom left of Room 2).
- Agent at `books` (approx x=11, y=7) facing South. Saw nothing.
- `A` is at approx x=13, y=6. `K` is at x=11, y=9?
- Let's re-read the observation in Room 2.
- At Yellow Door facing East: Saw laptop (front-left), airplane (front-left), backpack (front-slight-left), books (front).
- Front-left is North-East. Books is East.
- So Laptop, Airplane, Backpack are North of Books. Candidates `F, L, O` are in the North part of Room 2. `K` is also North?
- Agent went to `books`. Rotated South. Saw *nothing*.
- Candidate `A` is in the South part of Room 2 (relative to the door line). If `books` is central/East, and facing South saw nothing, maybe `A` is hidden or empty space. But is it "unexplored"? The agent looked South. If `A` represents a location in the field of view that was empty, it's observed. If it's behind a wall or outside FOV, it's unobserved.
- FOV is 90 degrees. Facing South covers South-East to South-West.
- If `books` is at y=7, and `A` is at y=6, it should be visible if no obstruction.
- However, `A` is marked near the wall.
- What about Room 1 candidates: `H, I, B, G, M, J, C, N`.
- Agent path in Room 1:
- (0,0) -> Observe N (Nothing).
- Rotate E -> Observe E (Shoes, etc, Yellow Door).
- Jump to Yellow Door.
- Jump back. Rotate S -> Observe S (Blue Door).
- Jump to Blue Door.
- Areas of Room 1 NOT observed:
- West wall? Agent at (0,0) facing N (seen), E (seen). Behind (S) and Left (W) not seen from (0,0).
- Agent at Yellow Door (East wall) facing W (seen). Saw Blue Door (South).
- Did Agent see the West part of Room 1?
- From (0,0) facing N: Saw nothing.
- From (0,0) facing E: Saw shoes, etc.
- From Yellow Door facing W: Saw Blue Door (front-right/South). The center/left of FOV would be West/North-West. But the Agent rotated -90 to face South immediately after jumping back? No.
- Let's check transcript.
- "Jumped to yellow door... Rotate(-90)... Observe()".
- Rotate -90 from West is facing South.
- So from Yellow Door, agent faced South. Saw Blue Door.
- The view West (looking back across Room 1) was NOT done.
- The view North from Yellow Door was NOT done.
- The view West from (0,0) was NOT done.
- So the West side of Room 1 is largely unobserved.
- Candidates in West Room 1: `H, I, B, G, M, J`.
- `C, N` are near the bottom of Room 1 (near Blue Door).
- `D, P` are in Room 3 (West side).
- Let's evaluate specific points:
- `D, P`: In Room 3. Agent at `*` (shopping cart) facing West saw `red chair` and `desklamp`. `D, P` are likely these objects or space near them. This area is OBSERVED.
- `C, N`: Room 1, bottom. Near Blue Door. From (0,0) facing E, agent saw Blue Door (front-right). `C, N` might be in that sector. From Yellow Door facing S, agent saw Blue Door.
- `H, I, B`: Room 1, bottom-left corner. From (0,0) facing N (empty). Facing E (shoes, etc). `H, I, B` are to the West/South-West of (0,0)? If (0,0) is start, and Blue Door is South, then (0,0) is somewhat North of Blue Door. `H` is deep South-West?
- Let's look at the map coordinates again.
- Room 3 is bottom. Room 1 is middle.
- Start (0,0) is in Room 1.
- If Blue Door is South of Start, then Start is north of y=3.
- If Yellow Door is East of Start, Start is west of x=8.
- So Start is roughly x=2..6, y=4..6?
- From Start, facing North (up) saw nothing. So `G` (if North) should be seen? Or `G` is blocked? Or `G` is further North?
- `G` is at top-left of Room 1. If facing North saw nothing, maybe `G` is too far or empty.
- From Start, facing East saw Yellow Door.
- West of Start (candidates `M, J`?) was not seen.
- South-West of Start (`H, I, B`?) was not seen.
- `M, J` are in the middle of Room 1.
- `G` is top left.
- `H, I, B` are bottom left.
- `C, N` are bottom middle.
- `F, L, O` are top of Room 2. Observed from door? Saw "laptop, airplane, backpack". These map to candidates? Likely OBSERVED.
- `E` is right side of Room 2.
- `K` is left side of Room 2.
- `A` is bottom of Room 2.
- Conclusion on Room 1: The West side (`G, M, J, I, B, H`) has poorly been covered. Agent only looked N, E, S. Never W.
- Conclusion on Room 2: Agent looked East (from door) and South (from books). North part was seen from door. South part seen from books.
- Conclusion on Room 3: Agent looked South (from door), East (from cart), West (from cart). Pretty good coverage. `D, P` are West, seen.
- Candidates to select:
- `G` (North-West corner of Room 1): Unobserved (looked N saw nothing, but G is West of N line?). If G is at x=2, y=9 and Start is x=4, y=5. Facing N sees N. G is NW. NW is "Front-Left". From Start (0,0), Front-Left is typically in FOV?
- Wait, "Observe action... reports ... FOV 90". Front-Left is in FOV.
- If "No objects in field of view" means literally nothing (not even candidates), then G was not seen? Or G is just a point in space. The question asks for "candidates ... in unexplored/unobserved regions".
- If the region was scanned and reported empty, is it "unobserved"? No, it's observed as empty.
- But if the agent never looked in that direction?
- Agent never looked West in Room 1.
- `M, J` are West of start?
- `I, B, H` are South-West of start?
- `G` is North-West.
- If Start is (0,0) and facing North covers -45 to +45.
- West is -90.
- So West, North-West (-45 to -90), South-West (-135 to -90) are blind spots from Start.
- Later, Agent at Yellow Door (East wall) faced South. FOV South (-135 to -225 aka +135). Covers South. West is right of South (or left?). Facing South (180). Right is West (270/-90).
- Wait, Facing South. Right is West.
- Agent at Yellow Door, facing South. "Observe". Saw Blue Door (Front-Right).
- Front-Right of South is South-West.
- So the South-West corner of Room 1 (near Blue Door) was observed from Yellow Door.
- Blue Door is at x=6, y=3. Yellow Door at x=8, y=7.
- Ray from (8,7) to (6,3) is South-West.
- This covers `C, N`? `C, N` are near Blue Door.
- What about `I, B, H`? They are further West (x=0..2).
- From (8,7) facing South. Front is South. Front-Right is SW.
- Is `H` (x=0, y=4) visible?
- Angle from (8,7) to (0,4). Delta x = -8, Delta y = -3.
- Angle is atan(-3/-8) = 20 deg south of west.
- Bearing from South (270 or -90): To West is 90 deg right. To (0,4) is ~110 deg right.
- FOV is 90 deg (+/- 45).
- Facing South. Front-Right is -22.5 to -45? No.
- Bins: Front [-22.5, 22.5]. Front-Right [22.5, 67.5].
- Max right is 45 deg from center.
- If center is South (180). Max right is 225 (SW).
- West is 270.
- So West wall is NOT in FOV when facing South.
- Therefore, `H, I, B` (West wall area) are unobserved.
- `G` (North-West): From Start (0,0) facing North. FOV +/- 45 (NE to NW).
- If `G` is far West, it might be outside NW limit.
- If `G` is at x=2, y=9. Start x=4, y=5.
- dx = -2, dy = 4. Angle = atan(-2/4) = -26 deg.
- Within +/- 45. So `G` was likely in FOV of first observation.
- But report was "No objects". So `G` is in an "observed empty" region.
- However, `M, J` (West/Middle). dx = -large, dy = small. Likely outside FOV of North look.
- Likely outside FOV of South look (from Yellow Door).
- So `M, J` are unobserved.
- `H, I, B`: Definitely unobserved (too far West).
- `F, L, O` (Room 2 North): Observed from door.
- `E` (Room 2 East): Observed from door? "Books" is East. `E` is near books?
- `A` (Room 2 South): Agent looked South from books. Saw nothing. If `A` is in that region, it's observed-empty.
- `K` (Room 2 West/Center): Near door?
- `D, P` (Room 3 West): Observed from shopping cart facing West.
- Best candidates for "unexplored/unobserved": `H, I, B` (West Wall Room 1) and maybe `M, J` (West Center Room 1).
- Also `G`? If it was empty, it's observed.
- Let's check the map labels again.
- `G` is in top left corner.
- `M, J` in middle left.
- `I, B` in bottom left.
- `H` in bottom-most left.
- `A` in Room 2 bottom.
- `C, N` near Blue Door (observed).
- `D, P` Room 3 West (observed).
- `E` Room 2 East (near books, observed).
- `F, L, O` Room 2 North (near laptop/airplane, observed).
- `K` Room 2 Middle (near path to books? observed).
- So the main blind spot is the West side of Room 1.
- `H`, `I`, `B`, `G`, `M`, `J`.
- `G` was in North FOV? Start x=4, y=5. G x=2, y=9. Angle -26. Inside FOV.
- `M` x=3, y=6. Start x=4, y=5. dx=-1, dy=1. Angle -45. Boundary.
- `J` x=4, y=6. Start x=4, y=5. dx=0, dy=1. Angle 0. Front. Observed.
- Wait, `M` and `J` are next to each other.
- `I` x=2, y=5. Start x=4, y=5. dx=-2. Angle -90 (West). Not seen facing N. Not seen facing S (from Yellow Door).
- `B` x=3, y=5. Start x=4, y=5. dx=-1. Angle -90. Not seen.
- `H` x=1, y=4. Start x=4, y=5. dx=-3, dy=-1. Angle -160. Not seen.
- So `I, B, H` are definitely unobserved. `M` maybe. `G` likely observed.
- Candidates: I, B, H, M, G (maybe).
- Let's pick the most obvious ones. `I, B, H` are along the West wall which was never faced.
- `G` is also West wall.
- `M, J` are interior.
- `A` in Room 2? Agent looked South saw nothing. `A` is South. So observed.
- Let's list `I, B, H`.
- What about `C`? x=3, y=3. Start x=4, y=5. From Yellow Door (x=8, y=7) facing S. dx=-5, dy=-4. Angle ~230 (SW). Outside FOV (max 225). So `C` might be unobserved.
- `N` x=4, y=3. dx=-4, dy=-4. Angle 225. Boundary.
- `C` and `N` are west of Blue Door (x=6).
- So `C` is likely unobserved.
- List: `H, I, B, C`.
- `G`? If I assume Start (0,0) is relative to the room, but the map shows start `*` in Room 3? No, prompt said "treat your initial position as origin". This is the local frame. The `*` on map is current position.
- Current position `*` is in Room 3.
- Start was Room 1.
- So my analysis of Room 1 blind spots holds.
- West side of Room 1 is the main unobserved area.
- Points: B, C, G, H, I, M.
- Also A? (Room 2 South). If "No objects" means empty, it's observed.
- I'll go with the West Room 1 cluster.
- H, I, B, G, M, J, C, N.
- Let's refine.
- Start was (0,0). Saw N. Saw E.
- Moved E, Saw S.
- West was never seen.
- Points in West of Room 1:
- `G` (Top Left)
- `M` (Mid Left)
- `J` (Mid Left)
- `I` (Low Left)
- `B` (Low Left)
- `H` (Bottom Left)
- `C` (Bottom Left-Center)
- `N` (Bottom Center)
- `J` is at x=4. If start is x=4, `J` is North. Observed.
- `N` is at x=4. If start is x=4, `N` is South.
- From Yellow Door (x=8, y=7) facing S. `N` (x=4, y=3). dx=-4, dy=-4. Angle SW (225). Boundary. Maybe seen.
- `C` (x=3). Further West. Not seen.
- `B` (x=3). Not seen.
- `I` (x=2). Not seen.
- `H` (x=1). Not seen.
- `G` (x=2, y=9). From Start (x=4, y=5) facing N. dx=-2, dy=4. Angle -26 (NW). Seen.
- `M` (x=3, y=6). From Start facing N. dx=-1, dy=1. Angle -45 (NW). Boundary.
- So `I, B, H, C` are the strongest candidates.
- `M` is borderline.
- `G` is likely seen.
- Let's select `B`, `C`, `H`, `I`.
- Also `A`? Room 2 South. Agent at `books` (x=11, y=7) facing South. `A` (x=13, y=6). dx=2, dy=-1. Angle -26 (SE). In FOV of South look. Observed.
- So `A` is observed.
- What about `K`? Room 2 West (x=11, y=9). Agent at `books` (x=11, y=7). North of agent. Not seen from `books` (looked S).
- But seen from door? Door at x=8. `K` is front-right (NE) from door? Or Front? `Books` was Front. `K` is same x, higher y.
- From door (x=8, y=7) facing East. `K` (x=11, y=9). dx=3, dy=2. Angle ~33 deg. Front-Right.
- Report from Yellow Door: "shoes... rubberduck...". No wait, that was Room 1.
- Report from Yellow Door into Room 2: "laptop, airplane, backpack, books".
- Laptop (front-left), Airplane (front-left), Backpack (front-slight-left).
- `K` might be one of these? Or empty space near them.
- If `K` is not an object, is it unobserved?
- The region was observed (saw objects).
- So Room 2 North is observed.
- Conclusion: Blind spot is West Room 1.
- Set: B, C, H, I, M.
- I will include M as it's on the edge.
- And `G`? It's NW. Seen.
- `D, P` seen.
- `A` seen.
- `F, L, O, E, K` seen.
- `N` seen (boundary).
- Final check on `M`. x=3, y=6. Start x=4, y=5. dx=-1, dy=1. Angle -45.
- If FOV is strict <45? Or <=45?
- "[-45, -22.5) -> front-left". So -45 is included.
- So `M` is seen.
- `I` (x=2, y=5). dx=-2, dy=0. Angle -90. Not seen.
- `B` (x=3, y=5). dx=-1. Angle -90. Not seen.
- `H` (x=1, y=4). Not seen.
- `C` (x=3, y=3). Not seen.
- So `B, C, H, I` are the unobserved ones.

FINAL ANSWER:
```json
{
"unexplored": ["B", "C", "H", "I"]
}
```

THINK:
The agent is currently at the position of the `shoppingcart` in Room 3.
The agent's history:
1. Start (0,0) in Room 1 (bottom left room). Observed North (Empty).
2. Rotated East. Observed `shoes`, `rubberduck`, `alarmclock`, `yellow door` (East wall), `blue door` (South wall? No, previous t...

################
#########.F.L.O#
#########.....E#
##.G....#.K....#
##..MJ..#......#
##......#......#
##......+....A.#
##IB....########
##H.....########
######+#########
#..CN..#########
#......#########
#......#########
#......#########
#.....*#########
#...DP.#########
################

You rotated clockwise 180°. You observe:
• red chair: front-right, mid distance, facing left
• desklamp: front-slight-right, slightly far, facing left.
You have a maximum of 11 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 180°. You observe:
• red chair: front-right, mid distance, facing left
• desklamp: front-slight-right, slightly far, facing left.
You have a maximum of 11 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ...

The agent is at "shoppingcart" in Room 3, facing West.
1. Observation revealed "red chair" and "desklamp".
2. Missing objects: "pan", "bike".
3. Room 3 seems covered (East was empty, West has chair/lamp, North is door).
4. Next logical step is to return to Room 1 and check the West side, which was never observed.
5. To return, jump to "blue door".
6. "Blue door" is to the North (since the agent entered from North facing South).
7. Current orientation is West. North is to the Right.
8. So, rotate 90 degrees clockwise to face North. The blue door should be in view. (Wait, from shopping cart facing West, North is Right. Blue door is the entrance, so it is "behind" the initial entry vector, which was South. So yes, it is North).
9. Actually, simpler: The agent knows where the door is (North). From West, rotate 90 deg clockwise to face North.
10. Verify door visibility then jump? Or just Rotate and Observe to confirm path? The agent needs to see the object to jump.
11. So: Rotate(90), Observe().

The agent is at "shoppingcart" in Room 3, facing West.
1. Observation revealed "red chair" and "desklamp".
2. Missing objects: "pan", "bike".
3. Room 3 seems covered (East was empty, West has chair/lamp, North is door).
4. Next logical step is to return to Room 1 and check the West side, which w...

THINK:
The agent started at [0,0] in Room 1 facing North.
1. **Step 1**: Rotate(90) -> Face East. Observed:
* shoes: front-slight-right (SE?), slightly far (4-8m).
* rubberduck: front-right (SE?), mid (2-4m).
* alarmclock: front-left (NE?), mid (2-4m).
* yellow door: front-slight-right (East wall), slightly far.
* blue door: front-right (South wall), slightly far.
* Inference: Agent at [0,0]. Facing East.
* Alarmclock (front-left) -> roughly [2, 2].
* Rubberduck (front-right) -> roughly [2, -2].
* Yellow door (front) -> roughly [5, 0] or [6, 0] on East wall. Let's assume [5,0].
* Blue door (right) -> roughly [0, -5] or similar on South wall. Or maybe [2, -4]. Let's refine later.

2. **Step 2**: JumpTo(yellow door). Agent at Yellow Door (approx [5,0]). Facing East. Observed:
* laptop: front-left (NE), slightly far.
* airplane: front-left (NE), slightly far.
* backpack: front-slight-left (East-ish), slightly far.
* books: front (East), mid (2-4m).
* Inference: Room 2 is to the East.
* Books -> [8, 0].
* Backpack -> [8, 2].
* Laptop -> [7, 3].
* Airplane -> [6, 3].

3. **Step 3**: JumpTo(books). Agent at Books (approx [8,0]). Rotate(90) -> Face South. Observed nothing.
* Implies South of books is empty.

4. **Step 4**: Rotate(90) -> Face West. Observed Yellow Door (front, mid).
* Confirming Yellow Door is West of Books. Distance mid (2-4m). Consistent with [5,0] and [8,0] (dist 3).

5. **Step 5**: JumpTo(yellow door). Agent at Yellow Door ([5,0]). Rotate(-90) -> Face South. Observed Blue Door (front-right, mid).
* Facing South. Front-right is South-West.
* Blue door is mid distance (2-4m) to the SW.
* If Agent is at [5,0], SW is roughly [3, -2] or [2, -3].
* Earlier (Step 1), from [0,0] facing East, Blue Door was "front-right" (SE) and on "right wall" (South wall).
* Let's synthesize: Blue door is on the South wall of Room 1.
* From [0,0], it's SE. From [5,0], it's SW. This puts the Blue Door somewhere between x=0 and x=5, on a negative y coordinate. Let's estimate [2, -4].

6. **Step 6**: JumpTo(blue door). Agent at Blue Door (approx [2, -4]). Facing South. Observed:
* shoppingcart: front (South), slightly far (4-8m).
* red chair: front-right (SW), mid (2-4m).
* Inference:
* Shoppingcart -> [2, -9] (approx 5m South).
* Red chair -> [0, -6] (approx SW).

7. **Step 7**: JumpTo(shoppingcart). Agent at Shoppingcart ([2, -9]). Rotate(-90) -> Face East. Observed nothing.

8. **Step 8**: Rotate(180) -> Face West. Observed:
* red chair: front-right (NW), mid.
* desklamp: front-slight-right (West/NW), slightly far.
* Inference:
* From [2, -9] facing West.
* Red chair is NW. Consistent with [0, -6] vs [2, -9] (dx=-2, dy=+3).
* Desklamp is West/NW. Maybe [-2, -8].

9. **Step 9**: Rotate(90) -> Face North. Observed:
* bike: front-left (NW), slightly far.
* red chair: front-left (NW), mid.
* blue door: front (North), slightly far.
* Inference:
* From [2, -9] facing North.
* Blue door at [2, -4] is Front (North). Distance 5. Matches "slightly far".
* Red chair at [0, -6] is NW. Front-left. Matches.
* Bike is Front-left (NW). Further than chair? "Slightly far". Maybe [-1, -5] or [0, -4].

10. **Missing Objects**: Pan.
* The "pan" is the only object not yet seen (from list 1-12: shoes, shoppingcart, laptop, rubberduck, bike, airplane, pan, alarmclock, red chair, backpack, desklamp, books).
* Wait, I haven't seen "pan". I have seen "bike" just now.
* The prompt listed 12 objects. I have seen 11.
* Where is the pan?
* Room 1 West side was blind.
* Room 2 South side was empty.
* Room 3 East side was empty.
* Likely location for "pan" is Room 1 West.

11. **Coordinate Refinement**:
* Agent Start: [0, 0], North.
* Room 1:
* Alarmclock: [2, 2] (Front-left from E @ 0,0) -> Actually Front-Left from East is NE. So x>0, y>0. Let's say [2, 2].
* Rubberduck: [2, -2] (Front-right from E @ 0,0) -> SE. x>0, y<0.
* Shoes: [4, -1] (Front-slight-right from E @ 0,0). "North near rubberduck". If duck is [2,-2], shoes north of it? Maybe [2, -1] or [3, -1].
* Yellow Door: [5, 0].
* Blue Door: [2, -5].
* Room 2 (East of Yellow Door):
* Books: [8, 0].
* Laptop: [7, 2].
* Backpack: [8, 2].
* Airplane: [6, 2].
* Room 3 (South of Blue Door):
* Shoppingcart: [2, -10].
* Red Chair: [0, -7].
* Desklamp: [-2, -9].
* Bike: [-1, -6] (North of Red Chair, near Blue Door).

* Refining coordinates based on distance bins:
* 0,0 -> Yellow Door (Front-slight-right, slightly far ~5m). [5,0] is dist 5. OK.
* 0,0 -> Blue Door (Front-right, slightly far ~5m). [2,-5] is dist 5.4. OK.
* Yellow Door [5,0] -> Blue Door [2,-5] (mid ~3m?). Dist is sqrt(9+25)=5.8 (slightly far). Observation said "mid distance". This is a conflict.
* Let's check observation: "Jump to yellow door... Rotate... Observe blue door: front-right, mid distance".
* Front-right from South is SW.
* Mid distance is 2-4m.
* This implies Blue door is closer to Yellow door.
* Maybe Yellow is [3,0] and Blue is [1, -2]?
* Let's rescale.
* Start [0,0].
* Rot 90 (Face E). Yellow door "slightly far" (4-8). [5,0] fits.
* Blue door "slightly far" (4-8). [3, -4] fits (dist 5).
* From Yellow [5,0] facing South: Blue door [3, -4] is dx=-2, dy=-4. Relative: Right 2, Forward 4. Angle: atan(2/4) = 26 deg. Front-Right is 22.5-45. Matches. Distance: sqrt(20) = 4.47. "Slightly far". Observation said "mid". 4.47 is close to mid/slightly boundary. Let's adjust Blue to [4, -3].
* Blue [4, -3]. From [0,0]: dist 5. OK. From [5,0]: dist sqrt(1+9)=3.16 (Mid). OK.
* So Blue Door is approx [4, -3].

* Room 3 Objects relative to Blue Door [4, -3] (Face S):
* Shoppingcart: "Front, slightly far". South. Say [4, -8] (dist 5).
* Red Chair: "Front-right, mid". SW. Say [2, -5] (dist 2.8).
* Jump to Shoppingcart [4, -8]. Face West.
* Red Chair ([2, -5]) relative to [4, -8] facing W: dx=-2, dy=+3. Forward 2, Right 3. Bearing: Right-ish. Observation: "front-right". OK. Dist: sqrt(13)=3.6 (mid). OK.
* Desklamp: "Front-slight-right, slightly far". Facing W. Front-slight-right is WNW. dx huge, dy small positive. Say [0, -7]. Rel to [4,-8]: dx=-4, dy=+1. Dist 4.1. "Slightly far". OK.
* Face North (from [4, -8]).
* Bike: "Front-left, slightly far". Front=N, Left=W. NW.
* Red Chair ([2, -5]) is Front-Left (NW). OK.
* Bike is "North, near to red chair". If chair is [2, -5], Bike maybe [2, -3] or [1, -4].
* Blue door [4, -3] is Front. OK.

* Room 2 Objects relative to Yellow Door [5, 0] (Face E):
* Books: "Front, mid". [8, 0].
* Laptop: "Front-left, slightly far". NE. [7, 3].
* Airplane: "Front-left, slightly far". [6, 3].
* Backpack: "Front-slight-left, slightly far". [8, 2].

* Room 1 Objects relative to [0,0] (Face E):
* Alarmclock: "Front-left, mid". NE. [2, 2].
* Rubberduck: "Front-right, mid". SE. [2, -2].
* Shoes: "North, near rubberduck". [2, -1].

* Summary of Positions:
* Agent: [4, -8] (at shoppingcart). Facing North.
* Room 1:
* alarmclock: [2, 2]
* rubberduck: [2, -2]
* shoes: [2, -1]
* yellow door: [5, 0]
* blue door: [4, -3]
* Room 2:
* books: [8, 0]
* laptop: [7, 3]
* airplane: [6, 3]
* backpack: [8, 2]
* Room 3:
* shoppingcart: [4, -8]
* red chair: [2, -5]
* desklamp: [0, -7]
* bike: [2, -3]

* Facings:
* shoes: backward (seen from E) -> West.
* rubberduck: left (seen from E) -> North.
* alarmclock: backward (seen from E) -> West.
* laptop: forward (seen from E) -> East.
* airplane: right (seen from E) -> South.
* backpack: left (seen from E) -> North.
* shoppingcart: forward (seen from S) -> South.
* red chair: forward (seen from S) -> South. (Later seen facing left from W -> South. Seen facing backward from N -> South).
* desklamp: left (seen from W) -> South.
* bike: right (seen from N) -> East.

FINAL ANSWER:
```json
{
"agent": {"position": [4, -8], "facing": "north"},
"alarmclock": {"position": [2, 2], "facing": "west"},
"rubberduck": {"position": [2, -2], "facing": "north"},
"shoes": {"position": [2, -1], "facing": "west"},
"yellow door": {"position": [5, 0], "facing": "east"},
"blue door": {"position": [4, -3], "facing": "south"},
"books": {"position": [8, 0]},
"laptop": {"position": [7, 3], "facing": "east"},
"airplane": {"position": [6, 3], "facing": "south"},
"backpack": {"position": [8, 2], "facing": "north"},
"shoppingcart": {"position": [4, -8], "facing": "south"},
"red chair": {"position": [2, -5], "facing": "south"},
"desklamp": {"position": [0, -7], "facing": "south"},
"bike": {"position": [2, -3], "facing": "east"}
}
```

THINK:
The agent started at [0,0] in Room 1 facing North.
1. **Step 1**: Rotate(90) -> Face East. Observed:
* shoes: front-slight-right (SE?), slightly far (4-8m).
* rubberduck: front-right (SE?), mid (2-4m).
* alarmclock: front-left (NE?), mid (2-4m).
* yellow door: front-s...

{
  "agent": {
    "position": [
      4,
      -8
    ],
    "facing": "north"
  },
  "alarmclock": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "rubberduck": {
    "position": [
      2,
      -2
    ],
    "facing": "north"
  },
  "shoes": {
    "position": [
      2,
      -1
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      5,
      0
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -3
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      8,
      0
    ]
  },
  "laptop": {
    "position": [
      7,
      3
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      6,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      8,
      2
    ],
    "facing": "north"
  },
  "shoppingcart": {
    "position": [
      4,
      -8
    ],
    "facing": "south"
  },
  "red chair": {
    "position": [
      2,
      -5
    ],
    "facing": "south"
  },
  "desklamp": {
    "position": [
      0,
      -7
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      2,
      -3
    ],
    "facing": "east"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "north"
  }
}

{
  "shoes": {
    "position": [
      4,
      -1
    ],
    "facing": "west"
  },
  "shoppingcart": {
    "position": [
      4,
      -9
    ],
    "facing": "south"
  },
  "laptop": {
    "position": [
      10,
      1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      2,
      -1
    ],
    "facing": "north"
  },
  "bike": {
    "position": [
      2,
      -5
    ],
    "facing": "east"
  },
  "airplane": {
    "position": [
      12,
      3
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      0,
      -3
    ],
    "facing": "west"
  },
  "alarmclock": {
    "position": [
      2,
      1
    ],
    "facing": "west"
  },
  "red chair": {
    "position": [
      2,
      -7
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      12,
      1
    ],
    "facing": "north"
  },
  "desklamp": {
    "position": [
      -1,
      -8
    ],
    "facing": "south"
  },
  "books": {
    "position": [
      10,
      -1
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      4,
      -4
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      4,
      -9
    ],
    "facing": "north"
  }
}

THINK:
The agent is currently located at the "shoppingcart" in Room 3.
The agent just rotated to face North (global).
Current Observation:
- `bike`: front-left, slightly far, facing right.
- "front-left" implies relative coordinates roughly (+y, -x).
- "slightly far" is distance bin (4, 8]. Let's estimate roughly (x=-3, y=5).
- "facing right" relative to agent (who is facing North) means facing East (+x).
- `red chair`: front-left, mid distance, facing backward.
- "mid distance" is (2, 4]. Let's estimate (x=-2, y=3).
- "facing backward" relative to agent means facing South (-y).
- `blue door`: front, slightly far, on front wall.
- "front" implies roughly along +y axis (x=0).
- "slightly far" is (4, 8]. Let's estimate (x=0, y=5).
- "on front wall" implies facing South (-y) towards the room interior.

Local Frame construction:
- Agent is at (0,0) facing +y.
- Bike: (-x, +y). Let's pick (-4, 5). Facing: +x.
- Red chair: (-x, +y). Closer than bike. (-2, 3). Facing: -y.
- Blue door: (0, +y). (~5 units away). (0, 5). Facing: -y.

Constructing the JSON:
- Origin: "agent"
- Objects:
- "bike": position ~[-4, 5], facing "+x"
- "red chair": position ~[-2, 3], facing "-y"
- "blue door": position ~[0, 5], facing "-y"

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"bike": {
"position": [-4, 5],
"facing": "+x"
},
"red chair": {
"position": [-2, 3],
"facing": "-y"
},
"blue door": {
"position": [0, 5],
"facing": "-y"
}
}
}
```

THINK:
The agent is currently located at the "shoppingcart" in Room 3.
The agent just rotated to face North (global).
Current Observation:
- `bike`: front-left, slightly far, facing right.
- "front-left" implies relative coordinates roughly (+y, -x).
- "slightly far" is distance bin (4, 8]. Let'...

{
  "origin": "agent",
  "objects": {
    "bike": {
      "position": [
        -4,
        5
      ],
      "facing": "+x"
    },
    "red chair": {
      "position": [
        -2,
        3
      ],
      "facing": "-y"
    },
    "blue door": {
      "position": [
        0,
        5
      ],
      "facing": "-y"
    }
  }
}

{
  "red chair": {
    "position": [
      -2,
      2
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "bike": {
      "position": [
        -4,
        5
      ],
      "facing": "+x"
    },
    "red chair": {
      "position": [
        -2,
        3
      ],
      "facing": "-y"
    },
    "blue door": {
      "position": [
        0,
        5
      ],
      "facing": "-y"
    }
  }
}

{
  "bike": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  }
}

THINK:
The agent is currently in Room 3 (bottom-left area of the map, based on the * position). The agent is at the "shoppingcart" facing North.
The observed objects in Room 3 are "shoppingcart", "red chair", "desklamp", and "bike".
- Agent entered Room 3 via the "blue door" from Room 1.
- Room 3 layout: The map shows the agent at the bottom. The "blue door" is likely the '+' above the agent.
- Room 1 is the middle room connecting Room 2 (right) and Room 3 (bottom).
- Room 2 is to the right (East) of Room 1, connected by the "yellow door".

Candidates analysis:
- A, F: Located in the room to the left/west of the central room? Wait. Let's trace the path.
- Start (0,0) in Room 1.
- Saw "yellow door" (East) and "blue door" (South-East? No, "right wall" when facing East = South).
- Jumped to "yellow door" (East). Saw Room 2.
- Jumped to "books" in Room 2. Saw North-East part.
- Came back to Room 1 ("yellow door").
- Saw "blue door" (South). Jumped to it.
- Entered Room 3 (South of Room 1).
- Currently in Room 3.
- The map shows a room at the bottom (Room 3), a room in the middle (Room 1), and a room to the right (Room 2).
- The map also shows a room to the *left* (West) of the middle room? Or is Room 1 the big one on the left?
- Let's re-read the initial observations.
- Start Room 1. Rotate 90 (East). Saw "yellow door" (front/East) and "blue door" (right/South).
- This implies Room 2 is East of Room 1. Room 3 is South of Room 1.
- Looking at the map:
- Bottom room contains '*'. This fits Room 3 being South.
- The room above the bottom room must be Room 1.
- The room to the right of the middle room (Room 1) must be Room 2.
- Candidates E, I, C, K, B, L, D, G, J, F, A, H.
- Room 3 (Bottom): Contains *, H. The agent is at *, facing North. Saw "bike" (front-left), "red chair" (front-left), "blue door" (front). The blue door is the + leading to the room above. 'H' is in Room 3. The agent did a 360 scan effectively (North->East->West->North). H is likely observed.
- Room 1 (Middle): Contains F, A, G, J.
- Initial pos (0,0). Saw North (empty). Saw East (doors).
- West side of Room 1 was identified as a blind spot. Points F and A are in the West/South-West part of Room 1.
- J is near the door to Room 3. Likely observed.
- G is in the middle.
- Room 2 (Top Right?): Map shows a room to the right of the middle section.
- Connected by yellow door.
- Candidates: C, K, E, I, L, D, B?
- Wait, the map structure is:
- Bottom: Room 3 (Agent here).
- Middle: Room 1 (Above Room 3).
- Right: Room 2 (Right of Room 1).
- Is there a room to the Left of Room 1? The map shows a large area on the left (F, A, B, C, E...).
- Let's look at the walls.
- Room 3 is bottom center.
- Room 1 is above it.
- Room 1 seems to extend to the left (F, A) and top (C, E, I).
- Wait, the map shows 3 connected regions.
1. Bottom box (Room 3).
2. Top-Left L-shape or rectangle? (Room 1).
3. Top-Right box (Room 2).
- Let's re-verify the "Yellow door" position. Agent at (0,0) facing East saw Yellow Door "front" (East). So Room 2 is East of Room 1.
- Map: The room with F, A, G, J seems to be Room 1.
- The room with L, D seems to be Room 2?
- Let's look at the doors (+).
- One + connects Bottom and Middle (Blue Door).
- One + connects Middle and Right (Yellow Door).
- So:
- Room 3: Bottom. (Contains H).
- Room 1: Middle/Left. (Contains F, A, J, G, B, C, E, I?? No, look at the walls).
- Walls separate the Right area (L, D) from the Left/Center area.
- Walls separate the Bottom area from the Center area.
- So Room 1 is the large area containing F, A, J, G, B, C, E, I, K.
- Room 2 is the area containing L, D.
- The agent explored Room 2 (East). Saw "books", "laptop", "airplane", "backpack". Jumped to "books", looked South (empty). The candidates L and D are in Room 2.
- L is near the door. D is deep. "Books" was mid-distance. D might be observed? Or is D hidden?
- "Observe" covers 90 degrees.
- In Room 2, agent jumped to books (East side?), looked South (empty).
- Initial view from door: Saw objects front-left.
- L is in the South-West of Room 2. D is in the East.
- From "books", agent looked South (saw nothing). This suggests the South-East corner is empty.
- L is near the entrance. Likely observed from the door or from books.
- D is in the back.
- Room 1 (Center/Left):
- Initial scan: North (empty). East (doors).
- The area West (F, A) has NOT been observed.
- The area North (B, C, E, I, K) has NOT been thoroughly observed.
- Agent was at (0,0). Facing North (saw nothing). Facing East (saw doors).
- (0,0) is likely near J or G?
- If (0,0) is near J, then North is towards B, C.
- "No objects in field of view" facing North. This means B, C, K, E, I might be empty or out of range.
- But are they "unexplored"? Yes, if they were out of range or occluded.
- Facing East saw doors.
- West (F, A) was never looked at.
- North-West (B) was never looked at.
- Deep North (C, E, I, K) might be too far or blocked.
- Conclusion on Unexplored:
- F, A: Definitely unexplored (West side of Room 1).
- B, C, E, I, K: North side of Room 1. Only observed from the south end. If they are far, they are unexplored.
- L, D: Room 2. Agent was there. Scan might have missed some corners, but likely better covered than Room 1 West.
- H: Room 3. Agent did a full rotation. H is likely observed.

- Focusing on the prompt "Select the points that are located in unexplored/unobserved regions."
- Region West of Room 1 (F, A) is completely blind.
- Region North of Room 1 (C, E, I, K) was viewed from a distance (if (0,0) is South). But "No objects" was reported. If there are no objects, the *space* is observed?
- However, the map candidates represent *locations* to be explored.
- F and A are behind the agent's starting orientation and were never looked at.
- B, C, E, I, K are in the direction the agent looked but saw "nothing". This implies either empty space (observed) or range limit. Since standard rooms are often larger than range, deep corners are unobserved.
- But F and A are the most obvious blind spots.
- Let's look closer at Room 1 candidates.
- J is near the door to Room 3. Observed.
- G is central. Observed.
- B is North-West.
- F, A are West.
- C, E, I, K are North/North-East.
- Agent at (0,0) facing North saw "Nothing".
- If (0,0) is near J, and the room extends to E/I, then E/I are very far.
- But the most critical unvisited/unseen area is the West wall (F, A).
- Also, is Room 2 fully mapped? Agent went to "books", looked South. Initial view saw North-East. South-West (L) might be observed from door. D (East) might be observed.
- I will prioritize the clearly unobserved West side of Room 1.
- The "fog" usually implies areas not covered by the FOV cones.
- Room 1 West (F, A) - never faced West in Room 1.
- Room 1 North (C, E, I, K) - faced North, but distance limit? If room is large, yes.
- Room 2 South (L) - looked South from books? Books are usually against a wall. If books are on North/East wall, looking South sees L.
- Let's refine. The "No objects" facing North means the agent saw the floor/walls up to range.
- However, F and A require facing West.
- What about C, E, I, K? If they are far North, they might be unobserved.
- Given the constraint of 20 steps and minimizing cost, usually we identify the "next target".
- The question asks for points in unexplored regions.
- F and A are definitely unobserved.
- B is North-West.
- C, E, I, K are North.
- Let's select the most prominent unobserved clusters. F, A, B. Maybe C, E, I if the room is long.
- Looking at the ASCII map, the North part of Room 1 is quite large.
- Let's assume the question wants candidates in areas not yet covered by any FOV.
- FOV History:
- Room 1: North (from J?), East (from J?).
- Room 2: West (from Door), North-East (from Door), South (from Books).
- Room 3: South (from Door), East (from Cart), West (from Cart), North (from Cart).
- Room 3 is fully covered. (H is covered).
- Room 2: North-East covered. South covered. West (entrance) covered. L and D likely covered.
- Room 1:
- North covered? Saw "nothing".
- East covered? Saw doors.
- South covered? (Behind start).
- West covered? Never.
- So F, A are unobserved.
- What about B? West-North.
- What about C, E, I, K?
- If the agent is at J (Start), and faced North, it covers a cone.
- B (North West) might be outside the cone.
- C, E, I, K (Deep North) might be too far.
- But F, A are completely behind/side.
- I'll select F, A, and B as the primary unobserved set in Room 1. And possibly C, E, I, K.
- Usually, "unexplored" refers to the significant geometric unknowns.
- Let's stick to the clear blind spot: West of Room 1.
- Candidates: A, F.
- Also B is adjacent to the West wall.
- Let's include A, B, F.
- What about C, E, I, K? They are in the "North" corridor. Agent looked North and saw nothing. If there were candidates there, wouldn't they be "objects"? The candidates are abstract points for the probe.
- If I looked North and saw nothing, I know it's empty space (explored) OR it's darkness (unexplored).
- In these tasks, "No objects" usually means empty floor.
- So the space is "seen" but empty.
- However, the West direction was *never* faced.
- So A and F are the strongest candidates.
- B is North-West. Cone is [-45, 45]. West is -90. North-West is -45. It's on the edge.
- I will go with A, B, F.
- Also, Room 1 seems to have a large extension to the North.
- Let's check Room 2 again. Agent at Books (somewhere inside). Rotated South. Saw nothing.
- Did agent look North in Room 2? No. From door, looked East (Front). Saw Laptop/Airplane (North-East).
- Did agent look West in Room 2? From Books, looked West (saw yellow door).
- So Room 2 North-West might be a blind spot? (Upper wall).
- But main blind spot is Room 1 West.

- Let's re-eval the candidates provided in the map visually.
- Room 1 is the big region.
- F, A are in the bottom-left of Room 1.
- B is mid-left.
- C, K, E, I are top-right of Room 1.
- Agent at start (J?) looked North.
- If J is (0,0), then B, C, K, E, I are all North (positive Y).
- "No objects" means nothing to report.
- But F, A are West.
- I will select A, B, F.
- Wait, I see I missed checking the "pan" (7). It was not in the lists. It might be in Room 1 West.
- So F, A are definitely holding unknowns.
- Are C, E, I, K unexplored?
- If I stood at the bottom and looked North, and saw *nothing* (not even a back wall?), then my vision might have been limited.
- But usually "No objects" implies "I see the room and it is empty of objects".
- However, F and A are definitely in the blind sector.
- I will output A, B, F.
- Let's check C, E, I, K again. If the room is L-shaped, and I am at the bottom of the vertical bar, looking North sees the vertical bar.
- F, A are in the horizontal protrusion? No, F,A are on the left wall.
- The map looks like a large rectangular room (Room 1).
- I'll bet on the unrotated sectors.
- Room 1: West sector unvisited.
- Candidates in West sector: F, A.
- B is North-West.
- I will include A, B, F.
- What about C, E, I, K? They are far North.
- I'll stick to A, F, B.
- Actually, looking at the distribution:
- Room 1 (West): F, A.
- Room 1 (North-West): B.
- Room 1 (North-East): C, K, E, I.
- I saw North. I did not see West.
- So A, F, B are the most likely "unexplored".
- I will just report A, F.
- Wait, B is aligned with F and A vertically? No.
- Let's include A, B, F.
- Is there any other place?
- Room 3 is done.
- Room 2 is done (mostly).
- I will refine the selection to the most obvious: A, F.
- Wait, B is just above A. If I didn't see A, I probably didn't see B (if B is West-ish).
- Let's add B.
- What about C? It's further North.
- I'll output A, B, C, F.
- Wait, C is North. I looked North.
- If I select C, I am saying looking North didn't cover it.
- I'll stick to the directional argument. West was never faced. North was faced.
- Unexplored: A, B, F.
- Let's check K, E, I.
- If the room is really big, maybe I didn't see the end.
- But "minimize cost" implies I shouldn't go check empty space if I saw it was empty.
- So assume "No objects" means "Mapped as Empty".
- Therefore, only the un-faced directions are unmapped.
- West: A, F.
- B is somewhat West? Map shows B at x=... low.
- Let's guess A, F.
- Wait, I'll add B just in case.
- And looking at the map, there is a cluster C, E, I, K.
- Why are there so many candidates there? Maybe it's a separate "room" or alcove I couldn't see from J?
- Looking at the map, Room 1 has a wall notch near B?
- If there's a wall blocking the view to C, E, I, K...
- But I don't see internal walls in the ASCII map in Room 1.
- So I will assume North is cleared.
- West (A, F) is the answer.

- Re-evaluating based on "Fog Probe" usually asking for the fogged areas.
- Fog is where the agent hasn't looked.
- Agent at J looked North (FOV +/- 45).
- Agent at J looked East (FOV +/- 45).
- So sectors [45, 135] (East) and [-45, 45] (North) are clear.
- Sectors [135, 225] (South) and [225, 315] (West) are blocked/unseen.
- South is behind J (wall).
- West is F, A.
- What about B? B is at a similar X to A, F.
- J is at roughly x=6, y=6.
- F is x=2, y=7. A is x=3, y=7.
- Vector J->A is (-3, 1). Angle ~160 deg (North-West-West).
- Vector J->B is (-3, 4). Angle ~126 deg (North-West).
- FOV North is [-45, 45] from Y-axis. (i.e., 315 to 45 in standard math, or 0 +/- 45 egocentric).
- North-West is outside North FOV.
- So B is likely unobserved.
- What about C? C is (x=9, y=13). J=(6,6). Vector (3, 7). Angle ~23 deg. Inside North FOV.
- K is (11, 13). Vector (5, 7). Angle ~35 deg. Inside North FOV.
- E is (9, 14). Angle ~20 deg. Inside.
- I is (14, 14). Angle ~45 deg. Borderline.
- So C, E, K, I are likely observed (reported as "no objects").
- F, A, B are outside.
- So Unexplored: A, B, F.

FINAL ANSWER:
{
"unexplored": ["A", "B", "F"]
}

THINK:
The agent is currently in Room 3 (bottom-left area of the map, based on the * position). The agent is at the "shoppingcart" facing North.
The observed objects in Room 3 are "shoppingcart", "red chair", "desklamp", and "bike".
- Agent entered Room 3 via the "blue door" from Room 1.
- Room 3 la...

################
#########E....I#
#########C.K...#
##.....B#......#
##......#.L..D.#
##....G.#......#
##....J.+......#
##FA....########
##..H...########
######+#########
#......#########
#......#########
#......#########
#......#########
#.....*#########
#......#########
################

You rotated clockwise 90°. You observe:
• bike: front-left, slightly far, facing right
• red chair: front-left, mid distance, facing backward
• blue door: front, slightly far, on front wall
Assume your current facing direction is called "north":
• bike is north, near to red chair.
You have a maximum of 10 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• bike: front-left, slightly far, facing right
• red chair: front-left, mid distance, facing backward
• blue door: front, slightly far, on front wall
Assume your current facing direction is called "north":
• bike is north, near to red chair.
You have a maximu...

The agent is at "shoppingcart" in Room 3, facing North.
1. Observation revealed "bike" (front-left) and "blue door" (front).
2. "Bike" is a new object!
3. Missing object: "pan".
4. Found so far: shoes, shoppingcart, laptop, rubberduck, bike, airplane, alarmclock, red chair, backpack, desklamp, books. (11 objects found).
5. Total objects expected: 12. Only "pan" is missing.
6. The agent sees the "blue door".
7. Jump to "blue door" to return to Room 1.
8. From "blue door" (at boundary), the agent will be facing North (into Room 1).
9. The "pan" is likely in the unvisited West side of Room 1.
10. The agent started at (0,0) facing North (empty), then turned East. The West side was never scanned.
11. From "blue door" (on South wall of Room 1), facing North looks into the room.
12. The West side of Room 1 is to the Left.
13. So, jump to "blue door", then rotate -90 (or +270) to face West? Or just Observe from the door?
14. From the "blue door" facing North, the West area is "front-left" or "left".
15. If the agent observes from the "blue door" facing North, it might see objects in the West if they are within the 90 degree FOV (front-left).
16. Let's Jump to "blue door" and Observe first.

The agent is at "shoppingcart" in Room 3, facing North.
1. Observation revealed "bike" (front-left) and "blue door" (front).
2. "Bike" is a new object!
3. Missing object: "pan".
4. Found so far: shoes, shoppingcart, laptop, rubberduck, bike, airplane, alarmclock, red chair, backpack, desklamp, b...

THINK:
The agent has explored three rooms.
**Room 1:**
- Initial position (0,0), facing North.
- Facing East, observed: shoes, rubberduck, alarmclock, yellow door (East wall), blue door (South wall).
- The blue door is on the "right wall" when facing East (South), and "on front wall" when facing South (South).
- The yellow door is on the "front wall" when facing East (East).
- From blue door facing North (current):
- shoes: front (North).
- rubberduck: front-left (North-West).
- alarmclock: front-slight-left (North-West).
- yellow door: front-right (North-East).
- This creates a slight conflict or needs careful placement.
- Start (0,0).
- Facing East from (0,0): Shoes (front-slight-right), Rubberduck (front-right), Alarmclock (front-left).
- Shoes ~ E/SE.
- Rubberduck ~ SE.
- Alarmclock ~ NE.
- Wait, earlier log: "shoes: front-slight-right (E->SE?)", "rubberduck: front-right (E->SE?)", "alarmclock: front-left (E->NE?)".
- From Blue Door (facing North):
- Shoes: front (N).
- Rubberduck: front-left (NW).
- Alarmclock: front-slight-left (NW).
- Yellow door: front-right (NE).
- Let's triangulate.
- Blue door is likely South of origin. Yellow door is likely East of origin.
- If Blue door is at (2, -2) [hypothetical].
- If Yellow door is at (4, 0).
- From (0,0) facing East: Yellow door is front (East). Blue door is right (South).
- From Blue door facing North: Yellow door is front-right (NE). Consistent.
- Objects:
- Shoes: From (0,0) facing E -> slightly right (SE?). From Blue door facing N -> front (N).
- Intersection of SE from (0,0) and N from Blue Door (located South). This puts shoes roughly East of (0,0) and North of Blue Door. Maybe (2, -1)?
- Rubberduck: From (0,0) facing E -> front-right (SE). From Blue door facing N -> front-left (NW).
- SE from (0,0) and NW from Blue Door? This implies Rubberduck is between (0,0) and Blue Door. Maybe (1, -1)?
- Alarmclock: From (0,0) facing E -> front-left (NE). From Blue door facing N -> front-slight-left (NW? No, front-slight-left is N/NW).
- NE from (0,0). NW from Blue Door. Intersection is North of (0,0) and East of Blue Door's X.
- Wait, "alarmclock: front-left" when facing East means North-East.
- "alarmclock: front-slight-left" when facing North from Blue Door means North-North-West relative to door.
- This suggests Alarmclock is North of the Blue Door and North of (0,0)?
- If (0,0) is origin. Alarmclock is NE. Blue Door is S. From S, Alarmclock is N. Correct.
- Missing "Pan". It might be West of (0,0).

**Room 2 (through Yellow Door):**
- Entered via Yellow Door.
- Objects: Laptop, Airplane, Backpack, Books.
- Books are East of Yellow Door.
- Laptop, Airplane, Backpack are North-East of Yellow Door.

**Room 3 (through Blue Door):**
- Entered via Blue Door.
- Objects: Shoppingcart, Red Chair, Bike, Desklamp.
- Shoppingcart: South of Blue Door.
- Red Chair: South-West of Blue Door (front-right from North facing South).
- Bike: South-East of Blue Door (front-left from North facing South?? No, wait).
- From Shoppingcart (facing North): Bike is front-left (North-West). Blue door is front (North).
- If Shoppingcart is South of Door. North is Door. Bike is NW of Cart -> West of Door.
- Earlier: "bike: front-left, slightly far, facing right" from Cart facing North.
- Earlier: "red chair: front-right" from Cart facing West (means North-West of Cart).
- Earlier: "desklamp: front-slight-right" from Cart facing West (North-West).

**Refining Coordinates:**
- **Agent**: Currently at Blue Door. Position roughly (2, -4) or similar? Let's fix origin.
- **Room 1**:
- Agent Start: (0,0).
- Yellow Door: (4, 0). On East Wall.
- Blue Door: (2, -4). On South Wall. (Example coords).
- Shoes: (3, -2).
- Rubberduck: (3, -3).
- Alarmclock: (1, -1).
- "Pan" is missing.
- **Room 2**:
- East of Yellow Door (4,0).
- Books: (7, 0).
- Laptop, Airplane, Backpack: North of Books/Door vector?
- From Yellow Door facing East: Laptop/Airplane/Backpack are front-left (NE).
- Laptop: (6, 2).
- Airplane: (6, 3).
- Backpack: (5, 2).
- **Room 3**:
- South of Blue Door (2, -4).
- Shoppingcart: (2, -7).
- From Cart facing West: Red chair (front-right -> NW), Desklamp (front-right -> NW).
- Red Chair: (0, -5).
- Desklamp: (0, -6).
- From Cart facing North: Bike (front-left -> NW).
- Bike: (0, -5)? Close to Red Chair.
- "bike is north, near to red chair".
- So Bike (0, -4), Red Chair (0, -5).
- Blue Door is at (2, -4). Bike/Chair are West of it.

**Status of Pan**:
- Not found in Room 2 (scanned North part, South part empty).
- Not found in Room 3 (scanned East part empty, West part has Bike/Chair/Lamp).
- Not found in Room 1 (East part has Shoes/Duck/Clock).
- Must be in West part of Room 1.
- Agent is at Blue Door facing North.
- West part of Room 1 corresponds to "front-left" or "left" from Blue Door.
- Observation from Blue Door facing North: Shoes (front), Rubberduck (front-left), Alarmclock (front-slight-left), Yellow door (front-right).
- "Rubberduck: front-left" (NW).
- "Alarmclock: front-slight-left" (N-NW).
- The West-most area (true West of 0,0) might still be hidden if FOV is 90 deg (cone).
- From Blue Door (2, -4) facing North:
- Cone covers NW to NE.
- True West of (0,0) would be at (-X, 0).
- From (2, -4), (-2, 0) is North-West.
- Pan might be there but blocked or just missed?
- Or Pan is "West" of Blue Door in Room 1?
- Wait, "rubberduck: front-left" is observed.
- Previous log: "You observe: No objects in field of view" at start (0,0) facing North.
- Pan must be at (West, North) relative to start? Or (West, South)?
- If it's at (-2, 0), from (0,0) facing North it's Left (invisible).
- From (0,0) facing East it's Behind (invisible).
- From Blue Door (2, -4) facing North, it's Front-Left (visible?).
- If it wasn't reported in the last Observe(), maybe it's further West or blocked.
- OR, I missed it.
- Re-read last Observe(): "shoes, rubberduck, alarmclock, yellow door". No Pan.
- So Pan is likely in the top-left (North-West) corner of Room 1, which might be "far" from Blue Door or occluded.
- Or "left" of (0,0).
- Agent needs to look at the West wall of Room 1.
- From Blue Door, move to an object in Room 1 and look West.
- Jump to Alarmclock (likely central/North) and look West?
- Or Jump to Rubberduck and look West?
- Alarmclock is "front-left" from (0,0) facing East (so NE). Wait.
- Let's re-verify Alarmclock position.
- Start (0,0) facing North. Empty.
- Rotate 90 (East). Alarmclock: front-left (NE).
- This means Alarmclock is at (+x, +y).
- Jump to Alarmclock?
- If Alarmclock is at (2, 2). Looking West from there sees (-x, 2).
- Looking South sees Blue Door.
- Looking North sees North wall.
- Pan is likely West of (0,0).
- So Jump to Alarmclock, Rotate to face West.

Wait, "rubberduck: front-right" from (0,0) facing East (SE).
"shoes: front-slight-right" (E-SE).
"alarmclock: front-left" (NE).

If I Jump to Alarmclock (NE), I can look West towards the (0,0) and beyond area.
This seems the best bet to find the Pan.

Let's produce the map with current estimates.
Agent: at "blue door".
Door coords need to be integers.
Let's assume:
Start (0,0).
Alarmclock (2, 2).
Yellow Door (4, 0).
Rubberduck (2, -2).
Shoes (4, -2).
Blue Door (2, -4).

Checks:
From (0,0) East:
- Alarmclock (2,2) is Front-Left (Left of East is North). correct.
- Yellow Door (4,0) is Front. correct.
- Rubberduck (2,-2) is Front-Right. correct.
- Shoes (4,-2) is Front-Right. correct.

From Blue Door (2,-4) facing North:
- Alarmclock (2,2) is Front. (Observed: front-slight-left. Maybe Clock is (1,2)).
- Yellow Door (4,0) is Front-Right. correct.
- Rubberduck (2,-2) is Front. (Observed: front-left. Maybe Duck is (0,-2)).
- Shoes (4,-2) is Front-Right. (Observed: front. Maybe Shoes is (2,-2) and Duck (0,-2)?).

Refined Room 1:
Alarmclock (1, 2).
Yellow Door (4, 0).
Blue Door (2, -4).
Rubberduck (0, -2).
Shoes (2, -2).

Check From (0,0) East:
- Alarmclock (1,2): Bearing from (0,0) is ~63 deg. FOV is [-45, 45]. Wait.
- Facing East is 0 deg relative to action. North is +90.
- (1,2) is +63 deg. Bin: "front-left" (22.5 to 45? No. >45 is Left).
- Bins: [-45, -22.5) FL, [-22.5, 0) FSL, [0, 22.5] FSR, (22.5, 45] FR.
- Note says: "Egocentric angle bins... [-45°,-22.5°)→front-left ... otherwise→beyond-fov."
- Wait. Field of view is 90 degrees? "Field of view: 90°". Usually means +/- 45.
- If Alarmclock is at (1,2), angle is atan2(2,1) = 63 deg. This is > 45. Should be invisible from (0,0) facing East.
- BUT it was seen. "front-left".
- Maybe "front-left" bin is wider?
- "[-45°,-22.5°)→front-left"
- The instructions say "otherwise -> beyond-fov".
- Maybe my angle calculation is relative to North?
- "Relationship reporting: ... 0° is front."
- If facing East, Front is East.
- (1,2) is North-East. Angle is +63 deg (Left).
- This should be out of view if FOV is +/- 45.
- Maybe Alarmclock is (2, 1)? Angle atan2(1,2) = 26 deg.
- 26 deg is "front-left" (22.5 to 45). Yes.
- So Alarmclock is roughly (2, 1).

Check From Blue Door (2, -4) facing North:
- Alarmclock (2, 1). Relative: (0, 5). Angle 0. Bin: Front.
- Observed: "front-slight-left". Maybe (1, 1).
- Relative from (2,-4) to (1,1) is (-1, 5). Angle atan2(-1, 5) = -11 deg.
- -11 deg is "front-slight-left". Yes.
- So Alarmclock at (1, 1).

Check Rubberduck.
From (0,0) East: Seen "front-right" (22.5 to 45 Right).
- Right is negative angle? "Positive = clockwise".
- East is 0. Right is South.
- Object at (x, -y).
- Angle should be +22.5 to +45 (Clockwise).
- Try (2, -1). Angle atan2(1, 2) = 26 deg. Correct.
- So Rubberduck ~ (2, -1).
- From Blue Door (2, -4) facing North.
- Relative to (2, -1) is (0, 3). Angle 0.
- Observed: "front-left".
- Needs to be Left of North. So x < 2.
- Try Rubberduck (1, -1).
- From (0,0) East: (1, -1). Angle 45. Borderline.
- From Blue Door (2, -4) North: (-1, 3). Angle atan2(-1, 3) = -18 deg. Front-Slight-Left.
- Observed: "front-left" (<-22.5). Needs angle < -22.5.
- Try (-1, 3) -> angle -18. Not enough.
- Try (0, -1).
- From (0,0) East: (0, -1) is South. 90 deg. Out of view.
- Maybe Blue Door is further East? (3, -4)?
- Let's stick to topological constraints mostly.

Room 1:
- Alarmclock (NE).
- Yellow Door (E).
- Shoes (SE).
- Rubberduck (S of Shoes? or W of Shoes?).
- Blue Door (S).

Room 2:
- Laptop, Airplane, Backpack (NE).
- Books (E).

Room 3:
- Shoppingcart (S).
- Red Chair (SW).
- Bike (SW/W).
- Desklamp (W).

Missing: Pan.
Likely West of (0,0).

Agent is at Blue Door.
To see West of (0,0), Jump to Alarmclock (1,1) and look West?
Or Jump to Rubberduck (if possible) and look West?
Alarmclock is a good vantage point for the NW corner.

FINAL ANSWER:
```json
{
"grid": "approximate",
"agent": {"position": [2, -4], "facing": "north"},
"shoes": {"position": [4, -2], "facing": "backward"},
"rubberduck": {"position": [2, -2], "facing": "left"},
"alarmclock": {"position": [1, 1], "facing": "backward"},
"yellow door": {"position": [4, 0], "facing": "east"},
"blue door": {"position": [2, -4], "facing": "south"},
"laptop": {"position": [6, 2], "facing": "forward"},
"airplane": {"position": [6, 3], "facing": "right"},
"backpack": {"position": [5, 2], "facing": "left"},
"books": {"position": [7, 0], "facing": "west"},
"shoppingcart": {"position": [2, -7], "facing": "forward"},
"red chair": {"position": [0, -7], "facing": "forward"},
"bike": {"position": [0, -6], "facing": "right"},
"desklamp": {"position": [0, -8], "facing": "left"}
}
```

THINK:
The agent has explored three rooms.
**Room 1:**
- Initial position (0,0), facing North.
- Facing East, observed: shoes, rubberduck, alarmclock, yellow door (East wall), blue door (South wall).
- The blue door is on the "right wall" when facing East (South), and "on front wall" when facing Sou...