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: television, 2: chair, 3: truck, 4: bike, 5: backpack, 6: pan, 7: cap, 8: lamp, 9: vase, 10: shelf, 11: rubberduck, 12: laptop
Doors: green 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 exploration has just begun. I am currently located at the origin (0, 0) in Room 1, facing North. I have not observed any objects or doors yet. According to the constraints, I cannot perform a `JumpTo` action in the first step as there are no previously observed objects. My goal is to map the environment with minimum cost. To do this, I need to gather information about my immediate surroundings. The most efficient first step is to perform an `Observe()` action to reveal objects and doors within my current 90° field of view (North). This will provide the necessary landmarks to plan subsequent movement or rotation.

The exploration has just begun. I am currently located at the origin (0, 0) in Room 1, facing North. I have not observed any objects or doors yet. According to the constraints, I cannot perform a `JumpTo` action in the first step as there are no previously observed objects. My goal is to map the env...

THINK:
The agent is at [0, 0] facing North.
Observations:
- Lamp: Front (North), mid distance (approx 3 units). Estimated position: [0, 3].
- Bike: Front-right (North-East), mid distance. Estimated position: [2, 2]. Facing "left" relative to agent (West).
- Blue door: Front-right, slightly far, on front wall (North wall). Estimated position: [2, 5].

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"blue door": {"position": [2, 5]}
}
```

THINK:
The agent is at [0, 0] facing North.
Observations:
- Lamp: Front (North), mid distance (approx 3 units). Estimated position: [0, 3].
- Bike: Front-right (North-East), mid distance. Estimated position: [2, 2]. Facing "left" relative to agent (West).
- Blue door: Front-right, slightly far, on f...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      2,
      5
    ]
  }
}

{
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

THINK: Based on the observation, I am at the origin facing North. The objects need to be placed in the local coordinate frame relative to me (+y forward, +x right).
1. **lamp**: "front, mid distance". "Mid distance" is (2, 4]. "Front" is around 0°. I'll place it at `[0, 3]`.
2. **bike**: "front-right, mid distance". "Front-right" is roughly 22.5° to 45°. Distance is (2, 4]. `[2, 3]` gives a distance of $\approx 3.6$ and angle $\approx 34^\circ$, which fits well. "facing left" means pointing towards my left (-x).
3. **blue door**: "front-right, slightly far, on front wall". "Slightly far" is (4, 8]. "On front wall" suggests it's on a wall perpendicular to my view (likely a horizontal wall at some +y). Let's estimate the wall is at $y=5$ or $y=6$. At `[3, 5]`, distance is $\approx 5.8$ (fits slightly far) and angle is $\approx 31^\circ$ (fits front-right).

Constructing the JSON map.

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

THINK: Based on the observation, I am at the origin facing North. The objects need to be placed in the local coordinate frame relative to me (+y forward, +x right).
1. **lamp**: "front, mid distance". "Mid distance" is (2, 4]. "Front" is around 0°. I'll place it at `[0, 3]`.
2. **bike**: "front-ri...

{
  "origin": "agent",
  "objects": {
    "lamp": {
      "position": [
        0,
        3
      ]
    },
    "bike": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "blue door": {
      "position": [
        3,
        5
      ]
    }
  }
}

{
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "lamp": {
      "position": [
        0,
        3
      ]
    },
    "bike": {
      "position": [
        2,
        3
      ],
      "facing": "-x"
    },
    "blue door": {
      "position": [
        3,
        5
      ]
    }
  }
}

{
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  }
}

THINK: [The agent is at position `*` facing North. The FOV is 90 degrees (45 degrees left and right of North). The observation reports a "blue door" on the "front wall" at "front-right". Based on the map, the "front wall" is the northern wall of the current room (Line 8), where there is a door `+` at relative coordinates (5, 5) from the agent (angle 45°). The observation of this door confirms that the agent can see up to 45 degrees to the right. The points `A` and `D` are clearly within the northern FOV. Point `F` is at relative coordinates (3, 3), which corresponds to exactly 45 degrees, placing it on the boundary of the FOV (likely observed). Points `E` (East, 90°), `B` (East-North-East, ~79°), and `C` (North-East, ~51°) are all outside the 45-degree wedge and thus in the unobserved region to the agent's right.]
FINAL ANSWER:
```json
{
"unexplored": ["B", "C", "E"]
}
```

THINK: [The agent is at position `*` facing North. The FOV is 90 degrees (45 degrees left and right of North). The observation reports a "blue door" on the "front wall" at "front-right". Based on the map, the "front wall" is the northern wall of the current room (Line 8), where there is a door `+` a...

###############
#......########
#......########
#......########
#......########
#......########
#......########
######+########
#D....C########
#.A.F..+......#
#......#......#
#.....B#......#
#*..E..#......#
#......#......#
########......#
###############

You observe:
• bike: front-right, mid distance, facing left
• lamp: front, mid distance
• blue door: front-right, slightly far, on front wall.
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:
• bike: front-right, mid distance, facing left
• lamp: front, mid distance
• blue door: front-right, slightly far, on front wall.
You have a maximum of 19 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I have successfully initiated the exploration by observing the initial view. I found a "blue door" on the front (North) wall, a "lamp" in front (North), and a "bike" to the front-right (North-East). The blue door is a key connectivity point. To continue mapping Room 1 and prepare to enter Room 2, I should move to the blue door.

Since I need to map the rest of Room 1 (which is behind me relative to the door's position on the North wall), I will jump to the door and then turn around (rotate 180 degrees) to face South. Observing from this position will allow me to see the central and southern parts of Room 1, which were previously behind me or outside my FOV. This action sequence maximizes information gain while moving towards a new room.

Plan:
1. `JumpTo(blue door)`: Move to the door to establish a new vantage point and prepare for room transition. Orientation remains North.
2. `Rotate(180)`: Turn to face South (back into Room 1).
3. `Observe()`: Map the previously unseen areas of Room 1 from this new position.

I have successfully initiated the exploration by observing the initial view. I found a "blue door" on the front (North) wall, a "lamp" in front (North), and a "bike" to the front-right (North-East). The blue door is a key connectivity point. To continue mapping Room 1 and prepare to enter Room 2, I ...

THINK:
Based on the previous observations and the current one:
1. **Initial Position:** (0,0), Facing North.
2. **Observation 1 (from 0,0 facing N):**
* `lamp`: Front, mid. Estimated at (0, 3).
* `bike`: Front-right, mid. Estimated at (2, 2). Facing Left (West).
* `blue door`: Front-right, slightly far, on front wall. Estimated at (3, 5).
3. **Action:** Jump to `blue door` (3, 5). Rotate 180 (Facing South).
4. **Observation 2 (from 3,5 facing S):**
* `green door`: Front-left, mid. Facing South, "left" is East. Position roughly (5, 3).
* `television`: Front-right, slightly far. Facing South, "right" is West. Position roughly (0, 1). Facing Left (East).
* `cap`: Front-slight-right, slightly far. Facing South, slightly West. Position roughly (2, 1). Facing Left (East).
* Proximity check: TV West of Cap matches "East" in inverted local frame.

All estimated coordinates fall within a reasonable integer grid for Room 1.

FINAL ANSWER:
```json
{
"agent": {"position": [3, 5], "facing": "south"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"blue door": {"position": [3, 5]},
"green door": {"position": [5, 3]},
"television": {"position": [0, 1], "facing": "east"},
"cap": {"position": [2, 1], "facing": "east"}
}
```

THINK:
Based on the previous observations and the current one:
1. **Initial Position:** (0,0), Facing North.
2. **Observation 1 (from 0,0 facing N):**
* `lamp`: Front, mid. Estimated at (0, 3).
* `bike`: Front-right, mid. Estimated at (2, 2). Facing Left (West).
* `blue door`: Fr...

{
  "agent": {
    "position": [
      3,
      5
    ],
    "facing": "south"
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      3,
      5
    ]
  },
  "green door": {
    "position": [
      5,
      3
    ]
  },
  "television": {
    "position": [
      0,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      2,
      1
    ],
    "facing": "east"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      5,
      5
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      5,
      5
    ],
    "facing": "south"
  }
}

THINK: [The agent is at the blue door, facing South (rotated 180° from initial North). The local frame is defined such that +y is the current facing direction (South), +x is to the right (West), and -x is to the left (East). The "television" is observed to the front-right (South-West) and "cap" to the front-slight-right (South-South-West). Based on the proximity note "television is east, near to cap" using the agent's facing as relative north, this confirms the television is to the right of the cap in the local frame (since relative East = Right). The "green door" is to the front-left (South-East). Estimated coordinates (x, y) in the local frame: television ~ (3, 5), cap ~ (1, 5), green door ~ (-2, 2). The objects are facing "left" relative to the agent, which corresponds to -x.]
FINAL ANSWER: {"origin": "agent", "objects": {"television": {"position": [3, 5], "facing": "-x"}, "cap": {"position": [1, 5], "facing": "-x"}, "green door": {"position": [-2, 2]}}}

THINK: [The agent is at the blue door, facing South (rotated 180° from initial North). The local frame is defined such that +y is the current facing direction (South), +x is to the right (West), and -x is to the left (East). The "television" is observed to the front-right (South-West) and "cap" to t...

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        3,
        5
      ],
      "facing": "-x"
    },
    "cap": {
      "position": [
        1,
        5
      ],
      "facing": "-x"
    },
    "green door": {
      "position": [
        -2,
        2
      ]
    }
  }
}

{
  "green door": {
    "position": [
      -1,
      2
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      3,
      6
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        3,
        5
      ],
      "facing": "-x"
    },
    "cap": {
      "position": [
        1,
        5
      ],
      "facing": "-x"
    },
    "green door": {
      "position": [
        -2,
        2
      ]
    }
  }
}

{
  "green door": {
    "position": [
      -1,
      2
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      3,
      6
    ],
    "facing": "east"
  }
}

You jumped to blue door. You rotated clockwise 180°. You observe:
• television: front-right, slightly far, facing left
• cap: front-slight-right, slightly far, facing left
• green door: front-left, mid distance, on left wall
Assume your current facing direction is called "north":
• television is east, near to cap.
You have a maximum of 18 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to blue door. You rotated clockwise 180°. You observe:
• television: front-right, slightly far, facing left
• cap: front-slight-right, slightly far, facing left
• green door: front-left, mid distance, on left wall
Assume your current facing direction is called "north":
• television is ea...

I am currently positioned at the blue door, facing South (looking back into Room 1). I have mapped the southern part of Room 1 and identified a "green door" on the left (East) wall. I previously identified the blue door on the North wall.
Since I am standing in the doorway of the blue door, I have the unique opportunity to see into the connected room (Room 2) by simply turning around. I have not yet seen what is inside Room 2.
To maximize information gain and minimize travel cost, I should inspect Room 2 from my current location before moving anywhere else.
Therefore, I will rotate 180 degrees to face North (into Room 2) and observe.

I am currently positioned at the blue door, facing South (looking back into Room 1). I have mapped the southern part of Room 1 and identified a "green door" on the left (East) wall. I previously identified the blue door on the North wall.
Since I am standing in the doorway of the blue door, I have t...

THINK:
Based on the observations:
1. **Initial Position (0,0), Facing North**:
* `lamp`: Front, mid distance (~3m) -> ~(0, 3).
* `bike`: Front-right, mid distance (~3m) -> ~(2, 2). Facing left (West).
* `blue door`: Front-right, slightly far (~5m). On front wall. Since I moved to it, let's place it at (1, 5).
2. **At Blue Door (1,5), Facing South**:
* `green door`: Front-left (SE). Mid distance (~3-4m). On left (East) wall. ~(4, 3).
* `cap`: Front-slight-right (SSW). Slightly far (~5m). ~(0, 0). Facing left (East, relative to South).
* `television`: Front-right (SW). Slightly far (~5m). ~(-2, 1). Facing left (East, relative to South). Relation: TV is West of Cap (consistent).
3. **At Blue Door (1,5), Facing North**:
* `vase`: Front-left (NW). Slightly far (~5m). ~(-2, 9).
* `rubberduck`: Front-slight-left (NNW). Slightly far (~5m). ~(0, 10). Facing left (West).

The agent is currently at the blue door (1, 5) facing North.

FINAL ANSWER:
```json
{
"agent": {"position": [1, 5], "facing": "north"},
"blue door": {"position": [1, 5]},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"green door": {"position": [4, 3]},
"cap": {"position": [0, 0], "facing": "east"},
"television": {"position": [-2, 1], "facing": "east"},
"vase": {"position": [-2, 9]},
"rubberduck": {"position": [0, 10], "facing": "west"}
}
```

THINK:
Based on the observations:
1. **Initial Position (0,0), Facing North**:
* `lamp`: Front, mid distance (~3m) -> ~(0, 3).
* `bike`: Front-right, mid distance (~3m) -> ~(2, 2). Facing left (West).
* `blue door`: Front-right, slightly far (~5m). On front wall. Since I moved to ...

{
  "agent": {
    "position": [
      1,
      5
    ],
    "facing": "north"
  },
  "blue door": {
    "position": [
      1,
      5
    ]
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      4,
      3
    ]
  },
  "cap": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      -2,
      1
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      -2,
      9
    ]
  },
  "rubberduck": {
    "position": [
      0,
      10
    ],
    "facing": "west"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  }
}

THINK:
The agent is currently positioned at the "blue door" facing North (into Room 2). The observation reveals a "vase" to the front-left and a "rubberduck" to the front-slight-left.
Based on the "slightly far" distance (4-8 units) and the bearing bins:
- `vase`: Front-left suggests an angle around -30° to -45°. Distance ~6. Coords approx (-3, 5).
- `rubberduck`: Front-slight-left suggests an angle around -10° to -20°. Distance ~6. Coords approx (-1, 6). Facing "left" relative to the agent (North) corresponds to West (-x).

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"vase": {"position": [-3, 5]},
"rubberduck": {"position": [-1, 6], "facing": "-x"}
}
}
```

THINK:
The agent is currently positioned at the "blue door" facing North (into Room 2). The observation reveals a "vase" to the front-left and a "rubberduck" to the front-slight-left.
Based on the "slightly far" distance (4-8 units) and the bearing bins:
- `vase`: Front-left suggests an angle around...

{
  "origin": "agent",
  "objects": {
    "vase": {
      "position": [
        -3,
        5
      ]
    },
    "rubberduck": {
      "position": [
        -1,
        6
      ],
      "facing": "-x"
    }
  }
}

{
  "vase": {
    "position": [
      -5,
      6
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -1,
      6
    ],
    "facing": "west"
  }
}

{
  "origin": "agent",
  "objects": {
    "vase": {
      "position": [
        -3,
        5
      ]
    },
    "rubberduck": {
      "position": [
        -1,
        6
      ],
      "facing": "-x"
    }
  }
}

{
  "vase": {
    "position": [
      -5,
      6
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -1,
      6
    ],
    "facing": "west"
  }
}

THINK: [The agent is at position (6, 7) facing North. The field of view is a 90-degree cone centered on North (from -45° to +45° relative to the Y-axis). Based on the coordinates extracted from the ASCII map:
- Agent `*`: (6, 7)
- `D`: (4, 8) -> dx=-2, dy=1. Angle ≈ -63°. Outside FOV (too far left).
- `E`: (3, 9) -> dx=-3, dy=2. Angle ≈ -56°. Outside FOV.
- `B`: (2, 10) -> dx=-4, dy=3. Angle ≈ -53°. Outside FOV.
- `F`: (2, 11) -> dx=-4, dy=4. Angle = -45°. On boundary, considered observed (likely the location of 'front-left' objects or empty space within FOV).
- `C`: (5, 9) -> dx=-1, dy=2. Angle ≈ -26°. Inside FOV.
- `A`: (3, 12) -> dx=-3, dy=5. Angle ≈ -31°. Inside FOV.
Points B, D, and E lie outside the 45-degree left limit of the agent's current North-facing view.]
FINAL ANSWER: {"unexplored": ["B", "D", "E"]}

THINK: [The agent is at position (6, 7) facing North. The field of view is a 90-degree cone centered on North (from -45° to +45° relative to the Y-axis). Based on the coordinates extracted from the ASCII map:
- Agent `*`: (6, 7)
- `D`: (4, 8) -> dx=-2, dy=1. Angle ≈ -63°. Outside FOV (too far left)....

###############
#......########
#..A...########
#.F....########
#.B....########
#..E.C.########
#...D..########
######*########
#......########
#......+......#
#......#......#
#......#......#
#......#......#
#......#......#
########......#
###############

You rotated clockwise 180°. You observe:
• vase: front-left, slightly far
• rubberduck: front-slight-left, slightly far, facing left.
You have a maximum of 17 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 180°. You observe:
• vase: front-left, slightly far
• rubberduck: front-slight-left, slightly far, facing left.
You have a maximum of 17 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am currently at the blue door, facing North into Room 2. I have observed a vase and a rubberduck to the front-left (West side) of Room 2. To ensure I fully map Room 2 and check for any additional connections (like a door to Room 3, though unlikely given the layout cues), I should enter the room. Jumping to the "vase" places me deeper inside Room 2. After jumping, I should turn around (Rotate 180°) to face South. This will allow me to see the "blue door" from the inside, confirming my path back, and view the rest of Room 2 which would be behind me if I stayed facing North.

I am currently at the blue door, facing North into Room 2. I have observed a vase and a rubberduck to the front-left (West side) of Room 2. To ensure I fully map Room 2 and check for any additional connections (like a door to Room 3, though unlikely given the layout cues), I should enter the room. J...

THINK:
Based on the sequence of observations and movements:
1. **Initial State**: Agent at (0, 0) facing North. Observed:
* **Lamp**: Front (North), mid distance. Estimated pos: (0, 3).
* **Bike**: Front-right (NE), mid distance, facing left (West). Estimated pos: (2, 2).
* **Blue Door**: Front-right, slightly far, on front wall (North). Estimated pos: (2, 5).
2. **At Blue Door (2, 5)**: Rotated to face South (back into Room 1). Observed:
* **Television**: Front-right (relative to South is West), slightly far, facing left (relative to South is East). Estimated pos: (-2, 2).
* **Cap**: Front-slight-right (SW), slightly far, facing left (East). Estimated pos: (-1, 2).
* **Green Door**: Front-left (SE), mid distance, on left wall (East). Estimated pos: (6, 3).
3. **At Blue Door (2, 5)**: Rotated to face North (into Room 2). Observed:
* **Vase**: Front-left (NW), slightly far. Estimated pos: (-2, 9).
* **Rubberduck**: Front-slight-left (NW), slightly far, facing left (West). Estimated pos: (0, 9).
4. **At Vase (-2, 9)**: Rotated to face South. Observed:
* **Chair**: Front-left (relative to South is East), slightly far, facing left (East). Estimated pos: (1, 6).
* **Backpack**: Front (South), near, facing forward (relative to South is South). Estimated pos: (-2, 7).
* (Blue Door visible again at (2, 5)).

Current State: Agent at **Vase (-2, 9)**, facing **South**.

FINAL ANSWER:
```json
{
"agent": {"position": [-2, 9], "facing": "south"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"blue door": {"position": [2, 5]},
"television": {"position": [-2, 2], "facing": "east"},
"cap": {"position": [-1, 2], "facing": "east"},
"green door": {"position": [6, 3]},
"vase": {"position": [-2, 9]},
"rubberduck": {"position": [0, 9], "facing": "west"},
"chair": {"position": [1, 6], "facing": "east"},
"backpack": {"position": [-2, 7], "facing": "south"}
}
```

THINK:
Based on the sequence of observations and movements:
1. **Initial State**: Agent at (0, 0) facing North. Observed:
* **Lamp**: Front (North), mid distance. Estimated pos: (0, 3).
* **Bike**: Front-right (NE), mid distance, facing left (West). Estimated pos: (2, 2).
* **Blue...

{
  "agent": {
    "position": [
      -2,
      9
    ],
    "facing": "south"
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      2,
      5
    ]
  },
  "television": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      -1,
      2
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ]
  },
  "vase": {
    "position": [
      -2,
      9
    ]
  },
  "rubberduck": {
    "position": [
      0,
      9
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -2,
      7
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      11
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      11
    ],
    "facing": "south"
  }
}

THINK:
I am currently at the position of the `vase` in Room 2, having just rotated 180 degrees. My previous orientation was North (when I observed the vase), so now I am facing **South** (global coordinates).

The `Observe()` output is relative to my current egocentric frame (Facing South).
- `chair`: front-left, slightly far, facing left.
- Front-left means positive Y (forward), negative X (left) in egocentric coordinates.
- "Slightly far" corresponds to distance (4, 8]. Let's approximate roughly.
- Egocentric facing: "facing left" relative to me. If I am facing South, my "left" is East. So the chair faces East. In local agent coordinates (+y is South), left is -x (East). So facing is -x.
- Let's assign rough local coordinates. Front-left ~ (-3, 5).
- `backpack`: front, near, facing forward.
- Front means +y axis (local). Near is (0, 2]. Let's say (0, 2).
- Facing forward means it faces the same way I am looking (South). In local coords, +y.
- `blue door`: front-left, slightly far, on front wall.
- Similar position to chair perhaps, or further. Front-left ~ (-2, 6).
- On front wall implies the wall I'm facing (South).

Let's refine coordinates based on bins:
- `chair`: front-left (-45 to -22.5 deg), slightly far (4-8m). Let's pick angle -30 deg, dist 6m. x = 6*sin(-30) = -3. y = 6*cos(-30) = 5.2. Integer: [-3, 5]. Facing "left" (local -x).
- `backpack`: front (-22.5 to 0 or 0 to 22.5, here likely 0), near (0-2m). Let's pick dist 2m. x = 0, y = 2. Integer: [0, 2]. Facing "forward" (local +y).
- `blue door`: front-left, slightly far. x ~ -3, y ~ 6.

JSON Construction:
Origin is "agent".
Objects:
- chair: pos [-3, 5], facing -x
- backpack: pos [0, 2], facing +y
- blue door: pos [-3, 6] (approx)

Wait, I need to be careful with "facing left".
Ego orientation: Forward is +y. Right is +x. Left is -x.
Object facing:
- Chair facing left -> facing -x direction.
- Backpack facing forward -> facing +y direction.

The instructions say: "Orientation: ... -When agent faces north: forward = north, right = east, etc."
Here agent faces South.
- Agent Forward = South.
- Agent Left = East.
- Chair faces left = Chair faces East. In local frame (where +y is South, +x is West?? No.)
Standard local frame definition:
+y: forward (South)
+x: right (West)
-x: left (East)
-y: backward (North)

Chair faces "left" (East). In local frame, left is -x. So facing: "-x".
Backpack faces "forward" (South). In local frame, forward is +y. So facing: "+y".

Positions:
Chair: Front-left. +y is forward, -x is left. So x is negative, y is positive.
Backpack: Front. x is 0, y is positive.
Blue door: Front-left. x negative, y positive.

Let's estimate integer positions.
Backpack: near (0-2). Front. (0, 2).
Chair: slightly far (4-8). Front-left. (-3, 6).
Blue door: slightly far (4-8). Front-left. (-2, 7).

Let's format the JSON.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"chair": {"position": [-3, 6], "facing": "-x"},
"backpack": {"position": [0, 2], "facing": "+y"},
"blue door": {"position": [-2, 7]}
}
}
```

THINK:
I am currently at the position of the `vase` in Room 2, having just rotated 180 degrees. My previous orientation was North (when I observed the vase), so now I am facing **South** (global coordinates).

The `Observe()` output is relative to my current egocentric frame (Facing South).
- `chair...

{
  "origin": "agent",
  "objects": {
    "chair": {
      "position": [
        -3,
        6
      ],
      "facing": "-x"
    },
    "backpack": {
      "position": [
        0,
        2
      ],
      "facing": "+y"
    },
    "blue door": {
      "position": [
        -2,
        7
      ]
    }
  }
}

{
  "backpack": {
    "position": [
      0,
      2
    ],
    "facing": "south"
  },
  "chair": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      -5,
      6
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "chair": {
      "position": [
        -3,
        6
      ],
      "facing": "-x"
    },
    "backpack": {
      "position": [
        0,
        2
      ],
      "facing": "+y"
    },
    "blue door": {
      "position": [
        -2,
        7
      ]
    }
  }
}

{
  "backpack": {
    "position": [
      0,
      2
    ],
    "facing": "south"
  },
  "chair": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  }
}

You jumped to vase. You rotated clockwise 180°. You observe:
• chair: front-left, slightly far, facing left
• backpack: front, near, facing forward
• blue door: front-left, slightly far, on front wall.
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 vase. You rotated clockwise 180°. You observe:
• chair: front-left, slightly far, facing left
• backpack: front, near, facing forward
• blue door: front-left, slightly far, on front wall.
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your though...

I am currently in Room 2 at the position of the 'vase', facing South. My goal is to explore the unvisited Room 3.
From my earlier observation in Room 1 (Step 2), I know there is a 'green door' on the East wall (reported as "left wall" when facing South).
To reach Room 3, I must travel back through the 'blue door' into Room 1, and then to the 'green door'.
My current view shows the 'blue door' is to the front-left. It is in my FOV and previously observed.
Action 1: `JumpTo(blue door)`. This places me at the threshold between Room 1 and Room 2. My orientation remains South.
From the 'blue door' facing South, I know the 'green door' is to the front-left (East). It is in my FOV (re-creating the view from Step 2).
Action 2: `JumpTo(green door)`. This moves me to the 'green door'. My orientation remains South.
Since the 'green door' is on the East wall, Room 3 is to the East. I am currently facing South. To look into Room 3, I need to rotate 90 degrees counter-clockwise (Left) to face East.
Action 3: `Rotate(-90)`. Now facing East.
Action 4: `Observe()`. This will reveal the contents of Room 3.

I am currently in Room 2 at the position of the 'vase', facing South. My goal is to explore the unvisited Room 3.
From my earlier observation in Room 1 (Step 2), I know there is a 'green door' on the East wall (reported as "left wall" when facing South).
To reach Room 3, I must travel back through t...

THINK:
I need to construct the JSON map based on all observations and movements relative to the initial origin (0,0) facing North (+y).

**Trajectory & Coordinates Tracking:**
1. **Start (Step 0):** (0,0), Facing North.
* Observed:
* `lamp`: Front, mid dist (~3u). Pos: (0, 3).
* `bike`: Front-right, mid dist. Pos: (2, 2). Facing Left (West).
* `blue door`: Front-right, slightly far. On front wall. Let's estimate (2, 5). Wait, "front wall" usually means the wall directly ahead. The door connects Room 1 (South) and Room 2 (North). Let's refine based on later jumps.
2. **Step 1:** Jump to `blue door`, Rotate 180 (face South).
* Agent is now at `blue door`. Let's assume the door is at (0, 5) or similar. Let's look at the geometry.
* Observation from `blue door` facing South (towards Room 1):
* `green door`: Front-left, mid dist, on left wall. Relative to South facing, front-left is South-East. Left wall is East wall. So `green door` is on the East wall.
* `television`: Front-right, slightly far. Relative to South, Front-Right is South-West. Facing Left (relative to object) -> facing West.
* `cap`: Front-slight-right, slightly far. Relative to South, South-West.
3. **Step 2:** Rotate 180 (face North), still at `blue door`.
* Look into Room 2.
* `vase`: Front-left, slightly far. Relative to North, North-West.
* `rubberduck`: Front-slight-left, slightly far. Relative to North, North-West.
4. **Step 3:** Jump to `vase`, Rotate 180 (face South).
* Agent at `vase`. Facing South.
* Observations:
* `chair`: Front-left, slightly far. Relative to South, South-East.
* `backpack`: Front, near. South of `vase`.
* `blue door`: Front-left, slightly far. Relative to South, South-East.
* Wait, previously `vase` was front-left (North-West) of `blue door` (facing North). So `blue door` must be South-East of `vase`. This matches.
5. **Step 4:** Jump `blue door` -> Jump `green door`, Rotate -90 (face East).
* Agent at `green door`. Facing East.
* Observations:
* `truck`: Front-right, slightly far. Relative to East, South-East.
* `pan`: Front-right, mid dist. South-East.
* `shelf`: Front-right, slightly far. South-East.

**Coordinate Estimation:**
Let's assign specific integer coordinates to satisfy the relational constraints.
* **Origin (0,0)** Facing North. Room 1.
* **Lamp**: (0, 3).
* **Bike**: (2, 2). Facing West.
* **Blue Door**: Let's place it at (0, 5) on the North wall.
* Initial view: "front-right, slightly far". (0,5) is purely Front (distance 5). "Front-right" suggests x > 0. Let's try **(2, 5)**. Distance $\sqrt{2^2 + 5^2} \approx 5.4$ (slightly far). Angle: atan(2/5) ~21 deg (front-slight-right). This fits.
* Let's check `blue door` position again. From (0,0) facing N, `blue door` is front-right. From `blue door` (2,5) facing S, `green door` is front-left (SE).
* If `green door` is on East wall, let's say x=5 or 6. SE of (2,5) means y < 5. Let's estimate `green door` at **(5, 2)**.
* Distance (2,5) to (5,2) is $\sqrt{3^2 + 3^2} \approx 4.2$ (mid/slight far border). Fits "mid distance".
* Bearing from (2,5) facing S: Vector (3, -3). Angle -45 deg (South-East). Relative to South (180), -45 is Left. Fits "front-left".
* **Room 1 Objects (from Blue Door (2,5) facing S):**
* `television`: Front-right (SW). Pos: (-1, 1)? Dist to (2,5) ~5. Angle fits.
* `cap`: Front-slight-right (S-slightly W). Pos: (1, 1)? Dist to (2,5) ~4. Angle fits.
* **Room 2 Objects (from Blue Door (2,5) facing N):**
* `vase`: Front-left (NW). Let's say **(0, 8)**.
* `rubberduck`: Front-slight-left (NW). Let's say **(1, 9)**.
* **Room 2 Objects (from Vase (0,8) facing S):**
* `chair`: Front-left (SE). Let's say **(3, 6)**?
* Bearing from (0,8) facing S to (3,6) is SE.
* `backpack`: Front (S). Near. Let's say **(0, 7)**.
* **Room 3 Objects (from Green Door (5,2) facing E):**
* `truck`: Front-right (SE). Let's say **(8, 0)**.
* `pan`: Front-right (SE). Let's say **(7, 1)**.
* `shelf`: Front-right (SE). Let's say **(9, -1)**.

**Refining Coordinates:**
Let's standardize.
Agent Start: (0,0).
Blue Door: (2, 5).
Green Door: (5, 2).

* **Observations from (0,0) N:**
* Lamp (0, 3).
* Bike (2, 2).
* **Observations from (2,5) S:**
* TV (-1, 1). Facing Left (West).
* Cap (0, 1).
* Green Door (5, 2).
* **Observations from (2,5) N:**
* Vase (-1, 8). Front-left (NW).
* Rubberduck (1, 9). Front-slight-left.
* **Observations from Vase (-1, 8) S:**
* Chair (2, 6). Front-left (SE). Facing Left (East? Wait. Relative to facing S, left is East. Facing Left means object faces East).
* Backpack (-1, 7). Front, near. Facing Forward (South).
* Blue Door (2, 5). Front-left (SE). Consistent.
* **Observations from Green Door (5, 2) E:**
* Truck (8, -1). Front-right (SE). Facing Backward (West).
* Pan (7, 0). Front-right (SE). Facing Forward (East).
* Shelf (9, -2). Front-right (SE).

Let's double check "Facing" directions.
* Bike: facing left (relative to agent facing N) -> West.
* TV: facing left (relative to agent facing S) -> East.
* Chair: facing left (relative to agent facing S) -> East.
* Backpack: facing forward (relative to agent facing S) -> South.
* Rubberduck: facing left (relative to agent facing N) -> West.
* Truck: facing backward (relative to agent facing E) -> West.
* Pan: facing forward (relative to agent facing E) -> East.

Final Coordinates Set:
Agent: (5, 2), Facing East.
Blue Door: (2, 5).
Green Door: (5, 2).
Lamp: (0, 3).
Bike: (2, 2), West.
TV: (-1, 1), East.
Cap: (0, 1).
Vase: (-1, 8).
Rubberduck: (1, 9), West.
Chair: (2, 6), East.
Backpack: (-1, 7), South.
Truck: (8, -1), West.
Pan: (7, 0), East.
Shelf: (9, -2).

Wait, "blue door: front-right, slightly far, on front wall" from (0,0).
If Blue Door is at (2,5), it's on the Y=5 line. Room 1 is Y < 5.
Green Door is on "left wall" (East) from Blue Door facing South. So Room 1 East wall is X=something.
If Green Door is at (5,2), then Room 1 is roughly X < 5.
This geometry (Room 1 roughly (0,0) to (5,5)) seems consistent.

Checking "From Green Door (5,2) facing East":
Truck at (8, -1) is SE. Correct.
Pan at (7, 0) is SE. Correct.

Wait, check TV facing.
Agent facing South. TV is front-right (SW). "facing left".
Relative to Agent (South), Left is East.
So TV faces East.

Check Chair facing.
Agent facing South. Chair is front-left (SE). "facing left".
Relative to Agent (South), Left is East.
So Chair faces East.

Check Truck facing.
Agent facing East. Truck is front-right (SE). "facing backward".
Relative to Agent (East), Backward is West.
So Truck faces West.

Check Pan facing.
Agent facing East. Pan is front-right (SE). "facing forward".
Relative to Agent (East), Forward is East.
So Pan faces East.

Check Backpack facing.
Agent facing South. Backpack is Front. "facing forward".
Relative to Agent (South), Forward is South.
So Backpack faces South.

Check Rubberduck facing.
Agent facing North. Rubberduck is front-slight-left. "facing left".
Relative to Agent (North), Left is West.
So Rubberduck faces West.

Check Bike facing.
Agent facing North. Bike is front-right. "facing left".
Relative to Agent (North), Left is West.
So Bike faces West.

One detail: Laptop?
The initial prompt listed objects: "12: laptop". I have not observed a laptop. I should not include it.

Final verification of positions for JSON:
Agent is at Green Door. Last action was Rotate, so position is (5,2). Facing East.
Doors are objects too? Yes, "blue door", "green door".
"Content: include all observed objects and gates; include the agent"

JSON Structure:
{
"agent": {"position": [5, 2], "facing": "east"},
"blue door": {"position": [2, 5]},
"green door": {"position": [5, 2]},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"television": {"position": [-1, 1], "facing": "east"},
"cap": {"position": [0, 1]},
"vase": {"position": [-1, 8]},
"rubberduck": {"position": [1, 9], "facing": "west"},
"chair": {"position": [2, 6], "facing": "east"},
"backpack": {"position": [-1, 7], "facing": "south"},
"truck": {"position": [8, -1], "facing": "west"},
"pan": {"position": [7, 0], "facing": "east"},
"shelf": {"position": [9, -2]}
}

Wait, need to check distance bins to refine integer coordinates.
Mid distance (2,4].
Slightly far (4,8].
Near (0,2].

Lamp: (0,0)->(0,3) dist 3 (mid). OK.
Bike: (0,0)->(2,2) dist 2.8 (mid). OK.
Blue Door: (0,0)->(2,5) dist 5.4 (slightly far). OK.

From Blue Door (2,5):
TV: (-1,1). Dist sqrt(3^2+4^2)=5 (slightly far). OK.
Cap: (0,1). Dist sqrt(2^2+4^2)=4.5 (slightly far). OK.
Green Door: (5,2). Dist sqrt(3^2+3^2)=4.2 (slightly far). OK. Note: Prompt said "mid distance" for Green Door in Step 2 observation ("green door: front-left, mid distance"). 4.2 is > 4 (slightly far). Maybe (4, 3)?
Let's try Green Door at (4, 3).
From (2,5) to (4,3): Dist sqrt(2^2+2^2) = 2.8 (mid). Fits better.
Bearing: (2,-2) is SE. Fits.
Agent at (4,3).
Truck (SE of 4,3): (7, 0) dist 4.2 (slightly far). OK.
Pan (SE of 4,3): (6, 1) dist 2.8 (mid). OK.

Let's update Green Door to (4, 3).
Agent final pos: (4, 3).

From Vase (-1, 8) to Chair (2,6):
Dist sqrt(3^2+2^2) = 3.6 (mid). Prompt said "slightly far" (>4).
Let's move Chair to (3, 5)? Dist sqrt(4^2+3^2)=5. OK.
Chair at (3,5).

Let's re-verify Backpack.
From Vase (-1, 8) facing S. Backpack is Front, Near.
(-1, 7) dist 1. Near. OK.

Let's re-verify Vase/Rubberduck from Blue Door (2,5).
Vase (-1, 8). Dist sqrt(3^2+3^2)=4.2 (slightly far). OK.
Rubberduck (1, 9). Dist sqrt(1^2+4^2)=4.1 (slightly far). OK.

Let's finalize the list.
Agent: (4, 3), East.
Blue Door: (2, 5).
Green Door: (4, 3).
Lamp: (0, 3).
Bike: (2, 2), West.
TV: (-1, 1), East.
Cap: (0, 1).
Vase: (-1, 8).
Rubberduck: (1, 9), West.
Chair: (3, 5), East.
Backpack: (-1, 7), South.
Truck: (7, 0), West. (Moved closer to keep relative distance consistent with pan/shelf).
Pan: (6, 1), East.
Shelf: (8, -1).

Wait, Truck "slightly far", Pan "mid distance".
If Agent (4,3).
Pan at (6,1): dist sqrt(2^2+2^2)=2.8 (mid). OK.
Truck at (7,0): dist sqrt(3^2+3^2)=4.2 (slightly far). OK.
Shelf at (8,-1): dist sqrt(4^2+4^2)=5.6 (slightly far). OK.

Looks solid.

FINAL ANSWER:
{
"agent": {"position": [4, 3], "facing": "east"},
"blue door": {"position": [2, 5]},
"green door": {"position": [4, 3]},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"television": {"position": [-1, 1], "facing": "east"},
"cap": {"position": [0, 1]},
"vase": {"position": [-1, 8]},
"rubberduck": {"position": [1, 9], "facing": "west"},
"chair": {"position": [3, 5], "facing": "east"},
"backpack": {"position": [-1, 7], "facing": "south"},
"truck": {"position": [7, 0], "facing": "west"},
"pan": {"position": [6, 1], "facing": "east"},
"shelf": {"position": [8, -1]}
}

THINK:
I need to construct the JSON map based on all observations and movements relative to the initial origin (0,0) facing North (+y).

**Trajectory & Coordinates Tracking:**
1. **Start (Step 0):** (0,0), Facing North.
* Observed:
* `lamp`: Front, mid dist (~3u). Pos: (0, 3).
...

{
  "agent": {
    "position": [
      4,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      2,
      5
    ]
  },
  "green door": {
    "position": [
      4,
      3
    ]
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "television": {
    "position": [
      -1,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      0,
      1
    ]
  },
  "vase": {
    "position": [
      -1,
      8
    ]
  },
  "rubberduck": {
    "position": [
      1,
      9
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      3,
      5
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      7
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      7,
      0
    ],
    "facing": "west"
  },
  "pan": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      8,
      -1
    ]
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  }
}

THINK: [The agent is at the green door facing East (local +y). The observed objects are the truck, pan, and shelf.
Relational constraints:
- Pan: front-right, mid-distance, facing forward (+y).
- Truck: front-right, slightly far, facing backward (-y).
- Truck is "North" (forward, +y) of Pan and "near" (dist <= 2).
- Shelf: front-right, slightly far.

Coordinates approximation (local x,y):
Front-right bin is (22.5°, 45°].
Candidate for Pan: x=2, y=3 (Distance ~3.6 -> mid). Angle atan(2/3) ~33.7° (fits).
Candidate for Truck: x=2, y=4 (Distance ~4.5 -> slightly far). Angle atan(2/4) ~26.6° (fits).
Distance(Pan, Truck) = 1 (fits "near").
Candidate for Shelf: x=3, y=4 (Distance 5 -> slightly far). Angle atan(3/4) ~37° (fits).

Orientation:
Pan faces forward (+y).
Truck faces backward (-y).
Shelf has no specified facing.]
FINAL ANSWER: {"origin": "agent", "objects": {"truck": {"position": [2, 4], "facing": "-y"}, "pan": {"position": [2, 3], "facing": "+y"}, "shelf": {"position": [3, 4]}}}

THINK: [The agent is at the green door facing East (local +y). The observed objects are the truck, pan, and shelf.
Relational constraints:
- Pan: front-right, mid-distance, facing forward (+y).
- Truck: front-right, slightly far, facing backward (-y).
- Truck is "North" (forward, +y) of Pan and "nea...

{
  "origin": "agent",
  "objects": {
    "truck": {
      "position": [
        2,
        4
      ],
      "facing": "-y"
    },
    "pan": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    },
    "shelf": {
      "position": [
        3,
        4
      ]
    }
  }
}

{
  "truck": {
    "position": [
      2,
      4
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      4,
      6
    ],
    "facing": "east"
  },
  "pan": {
    "position": [
      2,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "truck": {
      "position": [
        2,
        4
      ],
      "facing": "-y"
    },
    "pan": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    },
    "shelf": {
      "position": [
        3,
        4
      ]
    }
  }
}

{
  "truck": {
    "position": [
      2,
      4
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      4,
      6
    ],
    "facing": "east"
  },
  "pan": {
    "position": [
      2,
      2
    ],
    "facing": "east"
  }
}

THINK:
I am at the green door, facing East into Room 3.
My path has been: Room 1 (Origin) -> Blue Door (North) -> Room 2 -> Blue Door -> Green Door (East of Room 1) -> Room 3.
Let's reconstruct the layout.
Room 1 contains the origin. The Blue Door is on the North wall of Room 1. The Green Door is on the East wall of Room 1.
Room 2 is North of Room 1. I explored it (Vase, Backpack, Chair).
Room 3 is East of Room 1. I am currently looking into it.
The "Fog Probe" map shows:
Left room is Room 1 (width seems to be 7, x=1..7).
Top room is Room 2 (connected by '+' on top of Room 1).
Right room is Room 3 (connected by '+' on right of Room 1). The agent '*' is at the doorway between Room 1 and Room 3.
The candidates are in Room 3.
My current observation facing East (into Room 3) from the door:
- truck: front-right, slightly far
- pan: front-right, mid distance
- shelf: front-right, slightly far
FOV is 90 degrees (East). "Front-Right" means South-East relative to the map (since I am facing East).
So I can see the South-East part of Room 3.
Let's analyze the candidates A-F in the provided map:
The map coordinates (0,0) is bottom left.
Room 3 is the right-hand structure.
The agent '*' is at the door.
Facing East, "front" is East. "Right" is South. "Left" is North.
My FOV covers [-45, 45] relative to East (North-East to South-East).
However, the observation says objects are "front-right" (South-East).
Let's look at the candidate positions relative to the agent '*':
A: Located South-West of the center of Room 3? No, A is in the South-West corner of Room 3, just South of the door. If I face East, A is to my right (South). It might be obscured by the wall corner if it's "behind" the door frame, but usually, "front-right" covers this area if it's in front of the door plane. However, A is directly south of the door wall. It is likely in the "front-right" sector.
B: Located in the North-East part of Room 3. This is "front-left" or "front".
C: Located in the South-East part. This is "front-right".
D: Located in the South, closer to the middle. "front-right".
E: Located in the South-West corner? Similar to A.
F: Located in the far South-East corner.

Wait, let's look closer at the ASCII map.
The agent '*' is at the doorway.
The wall separates Room 1 (left) and Room 3 (right).
The candidates are inside Room 3.
A is near the West wall of Room 3 (south of the door).
B is near the North-East corner.
C is in the South-East area.
D is in the South area.
E is in the South-West area.
F is in the South-East corner.

My observation was:
- truck: front-right
- pan: front-right
- shelf: front-right
I have *seen* objects in the front-right direction.
The question asks for "unexplored/unobserved regions".
If I see objects in the front-right, does that mean I have observed the region? Yes.
What about "front-left"? I observed nothing in "front-left" or "front".
This implies either there is nothing there, or I saw empty space. Seeing empty space counts as observing.
However, usually "unexplored" means areas outside the current FOV or areas blocked by obstacles.
My FOV is 90 degrees. Facing East. I see North-East to South-East.
Region B is in the North-East (front-left/front). I reported no objects there, meaning I observed it and it's empty (or objects were too far/small, but for map purposes, I've looked there).
Region A, E, D, C, F are in the South (Right).
Wait, A and E are "behind" the door jamb if I am strictly in the doorway?
The door is on the wall. If I am *at* the door, facing East, my FOV is a cone expanding East.
The wall containing the door runs North-South.
Points strictly South of me (along the wall) are outside the 90-degree FOV (which is +/- 45 deg from East).
Points A and E look like they are close to the West wall of Room 3.
The angle to A or E from the doorway '*' would be roughly -90 degrees (South) or close to it.
My FOV extends to -45 degrees (South-East).
Therefore, the area directly South of the door (along the wall) is likely outside the FOV.
Let's verify the positions on the ASCII map.
`*` is at the door.
`A` is one step down, one step right?
Coordinates roughly:
Let `*` be (x, y).
A is at (x, y-2)? No, looking at lines:
Line with `*`: `#......*....B.#`
Line below: `#......#......#`
Line below: `#......#A.....#`
Line below: `#......#......#`
Line below: `#......#ED.C..#`
Line below: `########.....F#`

So A is 2 units South, 1 unit East of the door?
Angle = atan(dy/dx) = atan(-2/1) = -63 degrees.
My FOV is [-45, 45]. -63 is outside FOV. So A is unobserved.
E is lower down. 4 units South, 1 unit East. Angle even steeper. Unobserved.
D is 4 units South, 2 units East? atan(-4/2) = -63. Unobserved.
C is 4 units South, 4 units East? atan(-4/4) = -45. Boundary. Usually "front-right" is up to 45. It might be observed or unobserved. Let's look at the "front-right" bin definition.
"front-right" is (22.5, 45].
Wait, if it's beyond 45, it's "beyond-fov".
Since I saw objects in "front-right", I saw things in the (22.5, 45] cone (relative to East, so South-East).
Objects at angles > 45 degrees to the right (steeper South) are not seen.
Points A, D, E are likely > 45 degrees South.
Point F is deep South-East. 5 units South, 6 units East? atan(-5/6) ~ -40 deg. This is inside FOV.
Point B is North-East. 1 unit North? Inside FOV (Front-Left/Front). I saw nothing, so it's empty space, but "observed".
However, B is labeled in the map. Is it "unexplored"? I have looked at it.
So the "unexplored" ones are those outside the cone.
A, E, D are definitely South of the 45-degree line.
C is on the border.
Let's re-read the coordinates.
Door at Y.
A is Y-2. X+0 or X+1?
The map shows `*` aligned with `.` column. `A` aligned with `.` column.
Wait, `*` is between walls `#`.
The column of `*` is the doorway.
A is in the column *next* to the wall?
Let's assume the grid.
Row with *: `*` is at column X.
Row with A: `A` is at column X? No, `A` is `.` then `A`. It looks like it is inside Room 3.
Actually, look at the wall `#` to the left of A.
`#......#A.....#`
The wall is at column X-1. A is at column X.
If `*` is at column X (in the door), then A is same column, just south.
If A is directly South of `*`, the angle is -90 degrees.
This is definitely outside the +/- 45 degree FOV.
So A is unobserved.
Similarly E is directly South of A? `E` is next to `D`. `E` is at column X?
If E is column X, it's -90 deg. Unobserved.
D is column X+1? atan(dy/dx) for D: if dy is large and dx is small, it's > 45 deg.
Let's guess the coordinates from the ASCII art strictly.
`*` row index j. col index i.
A: row j+2 (down), col i. (Assuming rectangular grid). Angle -90. Unobserved.
E: row j+4, col i. Angle -90. Unobserved.
D: row j+4, col i+1. Angle atan(4/1) ~ 76 deg (to the right). Unobserved.
C: row j+4, col i+3. Angle atan(4/3) ~ 53 deg. Unobserved (cutoff is 45).
F: row j+5, col i+6? atan(5/6) ~ 40 deg. Observed.
B: row j, col i+5. Angle 0. Observed.

Wait, C: atan(4/3) = 53 degrees.
Is the cutoff strictly 45?
"Egocentric angle bins ... (22.5, 45] -> front-right, otherwise -> beyond-fov".
Yes, FOV is 90 degrees total, so +/- 45 degrees from center.
Any point with angle > 45 degrees from the facing direction (East) is unobserved.
Facing East (0 deg).
South is -90 deg.
Points with angle < -45 are unobserved.
A: (0, -2) -> -90 deg. Unexplored.
E: (0, -4) -> -90 deg. Unexplored.
D: (1, -4) -> atan(-4/1) = -76 deg. Unexplored.
C: (3, -4) -> atan(-4/3) = -53 deg. Unexplored.
F: (5, -5) -> atan(-5/5) = -45 deg. Edge case. If strictly -45, it is inside "front-right".
B: (5, 0) -> 0 deg. Inside.

So A, C, D, E are clearly outside FOV.
F is borderline.
Let's check the map again.
`#ED.C..#`
`########.....F#`
F is on the bottom row of the room.
The room height seems to be about 7 rows?
From `*` down to bottom wall:
`*`
`.`
`A`
`.`
`ED`
`F` is on the wall line? No, `F` is inside.
It seems F is very far South-East.
If F is at (6, -5), angle is -40. Inside.
If F is at (5, -6), angle is -50. Outside.
Looking at the ASCII:
`*` is top-left of Room 3.
F is bottom-right of Room 3.
Room 3 looks roughly square or slightly tall.
If it's square, the corner is 45 degrees.
If it's tall (height > width), the corner is > 45 degrees (outside FOV).
Counting characters:
Width of Room 3 (from wall to wall): `....B.#` is 7 chars.
Height of Room 3 (from top wall to bottom wall):
Row `*` (door)
Row `.`
Row `A`
Row `.`
Row `ED`
Row `F` (wait, F is in the last row of dots?)
Row `########` (bottom wall)
There are 5 rows of content below the door row?
Row 0: `*`
Row 1: `.`
Row 2: `A`
Row 3: `.`
Row 4: `ED.C..`
Row 5: `.....F`
So height is ~6 units. Width is ~7 units.
F is at (approx 6, 6). Angle ~45.
However, C is at (approx 4, 4). Angle ~45.
D is at (approx 2, 4). Angle ~63. Outside.
E is at (approx 1, 4). Angle ~76. Outside.
A is at (approx 1, 2). Angle ~63. Outside. (Assuming A is not strictly on the wall but 1 unit in).
Wait, look at A's position.
`#A.....#`
The wall is col 0. A is col 1.
`*` is at the door, usually aligned with the floor? Or the wall?
If `*` is the door, it replaces the wall character. So `*` is at col 0 relative to Room 3's interior?
If `*` is at x=0, and A is at x=0 (directly south), angle is 90.
If A is at x=1, angle is atan(y/x).
In the map:
`#......*`
`#......#A` -> A is shifted right? No.
Line 1: `#......*....B.#` (Wall, 6 dots, *, 4 dots, B, dot, Wall) -> * is at index 7.
Line 3: `#......#A.....#` (Wall, 6 dots, Wall, A, 5 dots, Wall).
So the wall is at index 7. A is at index 8.
Wait, `*` is at index 7. The wall below it is at index 7.
So `*` is in the doorway.
A is at index 8.
So dx = 1 (A is 1 unit East of the door line).
dy = 2 (A is 2 units South).
Angle = atan(2/1) = 63 deg.
Since I am facing East, 63 deg to the right is outside the 45 deg FOV.
So A is Unexplored.

Let's check D and E.
Line 5: `#......#ED.C..#`
Wall at 7. E at 8. D at 9.
dy = 4.
E: dx=1, dy=4. Angle atan(4) = 76 deg. Outside.
D: dx=2, dy=4. Angle atan(2) = 63 deg. Outside.
C: dot at 10. C at 11.
dx = 11-7 = 4. dy = 4. Angle atan(1) = 45 deg.
This is on the boundary.
Usually "front-right" is `(22.5, 45]`. So 45 is included in observed.
However, if it is slightly more than 45 (e.g. geometry variations), it might be out.
But strictly, 45 is observed.
Let's check F.
Line 6: `########.....F#`
Wait, line 6 is floor?
`########.....F#`
Wall at 0-7. Dots 8-12. F at 13.
dy = 5.
dx = 13 - 7 = 6.
Angle = atan(5/6) = 40 deg.
This is < 45 deg. So F is observed (in the front-right cone).

So A, E, D are definitely out.
C is border (likely observed).
F is observed.
B is observed.

However, consider the "unexplored regions" task.
Usually, points that are "behind the corner" are unexplored.
With a 90 deg FOV, anything > 45 deg is blind.
A (63 deg), E (76 deg), D (63 deg) are blind.
C (45 deg) -> technically observed.
F (40 deg) -> observed.
B (0 deg, dist ?) -> observed.

Wait, C is at x=4, y=4 relative to door.
Is it possible C is blocked by D or E?
No, we are points.
Is it possible C is considered "unexplored" because of the discrete grid?
Let's look at the example format. `["A", "C"]`.
I will stick to the geometric calculation.
Unexplored: A, D, E.
What about C?
If I have to choose, 45 degrees is usually the edge.
However, in many grid worlds, "front-right" might not cover the full diagonal if the agent is strictly axis-aligned.
But the definition says `(22.5, 45]`. So 45 is visible.
I will assume C is visible.
So, Unexplored: A, D, E.

Let me double check the map alignment for C.
Line with *: `...*....` (* at 7)
Line with C: `...#ED.C..#`
E at 8, D at 9, . at 10, C at 11.
dx = 11 - 7 = 4.
Row diff:
Row *: 0
Row .: 1
Row A: 2
Row .: 3
Row ED: 4
dy = 4.
Angle = 45.
So C is exactly on the edge.
Is it possible that the wall segment at (7, 1) blocks the view?
The wall is at x=7 for all rows below *.
I am at (7, 0).
To see (11, 4), the line of sight goes through (8,1), (9,2), (10,3).
The wall is at x=7. The open space starts at x=8.
So the line of sight is clear (all x >= 8).
So C is visible.

What about F?
Row F is next.
Row 5: `.....F`
F is at 13.
dy = 5. dx = 6. Angle 40. Visible.

So only A, D, E are clearly invisible.
Let's check if the question implies "visited"? No, "unexplored/unobserved".
So I just list the ones I haven't seen.
A, D, E.

Wait, is it possible B is unobserved?
B is at `...*....B.#`.
B is at x=12. dx=5. dy=0.
Angle 0. Front. Visible.

Result: A, D, E.

One small detail: `JumpTo` lands me "at the same position as the object".
I jumped to `green door`.
The green door is on the "left wall" of Room 1 (facing South), i.e., East wall.
So I am at the boundary of Room 1 and Room 3.
The map shows `*` at the boundary.
The logic holds.

Final check on C.
If the agent considers the center of the cell, and the target is the center of the cell.
Angle is exactly 45.
If the FOV is strictly < 45?
Instruction: `(22.5,45] -> front-right`. The bracket `]` means inclusive.
So C is observed.

Wait, is there any occlusion?
Objects "truck", "pan", "shelf" are observed.
Could they block the view?
"truck" and "pan" are "near" to each other.
They are objects, not full-height walls (usually). They don't occlude vision in this problem formulation unless specified.
So C is observed.

Therefore, the answer should be A, D, E.
I should confirm if I missed any.
Let's look at the order of A, B, C, D, E, F.
A: South-West. Blind.
B: North-East. Visible.
C: South-East (Edge). Visible.
D: South (Middle). Blind.
E: South-West. Blind.
F: South-East (Far). Visible.

Wait, looking at the map again...
`#......*....B.#`
`#......#......#`
`#......#A.....#`
The wall extends down from the door?
`#......#` at the start of the line means the left wall of Room 1.
`#` in the middle:
Line 1: `#......*....B.#` -> Middle `.`? No `*`.
Ah, the middle column is index 7.
`#` (0) `.` (1-6) `*` (7) `.` (8-11) `B` (12) `.` (13) `#` (14).
Line 3: `#......#A.....#` -> Wall at 7?
`#` (0) `.` (1-6) `#` (7) `A` (8) ...
Yes, there is a wall at x=7 below the door.
The agent is at (7, 0) relative to that local patch.
The wall is at (7, 1), (7, 2), etc.
The agent is at x=7.
To see A at (8, 2):
Line of sight from (7, 0) to (8, 2).
Passes through y=1. At y=1, x goes from 7 to 7.5?
Intersection with y=1 line: x = 7 + 0.5 * (1/2) = 7.25?
Wait, if I am at center of (7,0). A is center of (8,2).
Vector (1, 2).
At y=1 (center of cell (7,1) or (8,1)?), x = 7.5.
The cell (7,1) is a WALL `#`.
Does the wall block the view?
The wall fills the cell (7,1).
The line of sight goes through the edge of (7,1) and (8,1).
In integer grids, usually adjacent diagonals are visible?
Or does the wall at (7,1) block the view to (8,2)?
If (7,1) is a wall, and I am at (7,0), and target is (8,2).
The ray hits the corner of (7,1).
Usually, walls block diagonals if they are "hard" corners.
However, A is marked "unexplored" purely by angle in the previous analysis (63 degrees).
Occlusion would make it *more* unexplored.
What about C?
Vector (4, 4). Ray passes through (8,1), (9,2), (10,3).
(8,1) is `.` (empty).
(9,2) is `.` (empty).
(10,3) is `.` (empty).
So C is not occluded by walls.
And angle is 45. So C is visible.

Conclusion stands: A, D, E are the ones with angle > 45.

Wait, let's look at F again.
F is (6, 5). Angle 40. Visible.
But is it occluded?
Ray passes through (8, 0.83), (9, 1.6), etc.
Cells traversed: (8,1), (9,2), (10,3), (11,3), (12,4)...
Are there any obstacles?
`ED` is at row 4. E at 8, D at 9.
Ray to F passes near D?
F is at 13 (col) , row 5.
Ray from 7,0 to 13,5.
Slope 5/6 = 0.833.
At x=9 (D's col), y = 2 * 0.83 = 1.66.
D is at row 4. So ray is far above D (spatially "north" in the map, but "left" in agent view).
Wait, "North is Up".
Rows increase downwards in my manual parsing?
Usually "North is Up" means row index decreases as y increases.
Let's stick to the visual map.
Top is North.
`*` is North.
`A` is South of `*`.
`F` is South-East.
`D` is South.
Ray to F (South-East) goes through empty space in the middle of the room.
Obstacles `A`, `E`, `D` are hugging the West wall of Room 3.
So F is clear.

Final set: A, D, E.

Wait, is it possible `C` is considered unexplored?
If `front-right` is strictly `(0, 45]`, then 45 is inside.
If the agent faces East, 45 is South-East.
The cell C is exactly South-East.
I will assume it is Observed.

Double check "Fog Probe" instructions.
"Select the points that are located in unexplored/unobserved regions."
Based on FOV cone.
A, D, E are outside the cone.
B, C, F are inside (or on boundary).
Result: ["A", "D", "E"]

One alternate interpretation:
Maybe the door is at (7, 8) and Room 3 is "up"?
No, "North is Up".
Room 2 is above Room 1.
Room 3 is to the right of Room 1.
So the layout is confirmed.

Wait, look at the wall to the *left* of A.
`#......#A.....#`
The wall is at x=7.
If I am standing at x=7 (in the door), I am adjacent to the wall at x=7, y-1.
To see A at x=8, y-2.
This is a very sharp angle around the corner.
Usually, you cannot see around a corner > 45 degrees.
And 63 > 45.
So A is hidden.
Same for E, D.

What about C?
Angle 45. Corner visibility.
Usually, you can see the diagonal.
So C is visible.

Final Answer seems to be A, D, E.
I'll output this JSON.

Wait, is there any ambiguity about "unobserved"?
"candidates are located in... regions".
If a candidate is in a region I have *not* seen, it is unobserved.
I have not seen the region > 45 degrees to the right.
So A, D, E are unobserved.

One check: Did I observe "shelf" or "truck" or "pan" at these locations?
"truck": front-right, slightly far.
"pan": front-right, mid distance.
"shelf": front-right, slightly far.
"slightly far" is (4, 8].
"mid distance" is (2, 4].
C is at distance sqrt(4^2+4^2) = 5.6 -> "slightly far".
F is at distance sqrt(6^2+5^2) = 7.8 -> "slightly far" or "far".
Maybe "shelf" is C?
"truck" (slightly far) could be C or F?
"pan" (mid) could be closer?
Maybe something at (2, 2) or (3, 3)?
(2,2) dist 2.8 (mid). Angle 45.
(3,1) dist 3.1 (mid). Angle 18.
If I saw objects, they must be in the observed region.
This confirms the observed region exists and contains objects.
It doesn't change the fact that A, D, E are in the blind spot.

Final check:
Is C considered "blind" because it is behind the "pan" or "truck"?
The problem doesn't simulate complex occlusion by objects usually.
And "unexplored" usually refers to the map coverage (FOV).
So I stick to FOV geometry.

Unexplored: A, D, E.

Wait, looking closer at C.
If C is "slightly far" and I see a "shelf" at "slightly far", maybe C *is* the shelf?
If C is the shelf, then C is observed.
If C is *not* the shelf, but is in the same region, is it observed?
"Select the points that are located in unexplored/unobserved regions."
If C is in the FOV, the region is observed. Even if C itself is a hidden object (which we don't know), the *location* is in an observed region.
The question asks about the points/regions, not the specific object identity.
The region of C is within the FOV.
The regions of A, D, E are outside.

Final Answer: ["A", "D", "E"]

One edge case: "A" is very close. (1, 2). Distance 2.2 (mid).
If "A" was visible, I would have reported an object there if there was one.
But the angle prevents it.
So A is definitely unobserved.

FINAL ANSWER:
{
"unexplored": ["A", "D", "E"]
}

THINK:
I am at the green door, facing East into Room 3.
My path has been: Room 1 (Origin) -> Blue Door (North) -> Room 2 -> Blue Door -> Green Door (East of Room 1) -> Room 3.
Let's reconstruct the layout.
Room 1 contains the origin. The Blue Door is on the North wall of Room 1. The Green Door is on...

###############
#......########
#......########
#......########
#......########
#......########
#......########
######+########
#......########
#......*....B.#
#......#......#
#......#A.....#
#......#......#
#......#ED.C..#
########.....F#
###############

You jumped to blue door. You jumped to green door. You rotated counterclockwise 90°. You observe:
• truck: front-right, slightly far, facing backward
• pan: front-right, mid distance, facing forward
• shelf: front-right, slightly far
Assume your current facing direction is called "north":
• truck is north, near to pan.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to blue door. You jumped to green door. You rotated counterclockwise 90°. You observe:
• truck: front-right, slightly far, facing backward
• pan: front-right, mid distance, facing forward
• shelf: front-right, slightly far
Assume your current facing direction is called "north":
• truck i...

I am at the green door facing East into Room 3.
I see a truck, pan, and shelf, all generally front-right (South-East relative to the door).
I need to fully map Room 3. Simply observing from the door might miss objects in the corners or behind me once I enter.
To get a better view, I should jump to an object inside Room 3 and look back. The "pan" is at a mid distance, making it a good central pivot point.
Plan:
1. Jump to the `pan`.
2. Rotate to look at the rest of the room. Since the objects were front-right (South-East) and I was facing East, jumping to the pan puts me South-East of the door. To see the rest of the room (likely North and East parts), I should rotate. Let's orient North (relative to the room) or West to see the door back.
Actually, if I jump to the pan (which was front-right), and my orientation doesn't change (still East), the door is now behind-left.
To see the unseen parts of the room (which were to my left/front-left when standing at the door), I should rotate. Rotating 90 degrees (facing South) or -90 (facing North) might help.
Let's try rotating to face West (back towards the door) to confirm the room boundaries and see anything I missed in the "front-left" sector from the door's perspective (which is now my right). Or better, rotate to sweep the room.
If I jump to the pan and rotate 180 (facing West), I see the door. If I rotate -90 (facing North), I see the "left" side of the room I might have missed.
Let's jump to the `pan`, rotate -90 to face North (relative to global, which is 'left' relative to my current East facing? No. Current facing East. Rotate(-90) makes me face North).
From the door (facing East), the pan was front-right. So I am now in the South-East area. Facing North allows me to see the North-East and North-West corners of Room 3. This seems efficient.

I am at the green door facing East into Room 3.
I see a truck, pan, and shelf, all generally front-right (South-East relative to the door).
I need to fully map Room 3. Simply observing from the door might miss objects in the corners or behind me once I enter.
To get a better view, I should jump to a...

THINK:
I need to construct a global map based on the observations.
1. **Initial State**: Agent at (0,0), facing North (Room 1).
2. **Observation 1 (from 0,0 facing N)**:
* `bike`: front-right (NE), mid distance (approx 2-4 units). Let's estimate (2, 2) facing West (left).
* `lamp`: front (N), mid distance (approx 0, 3).
* `blue door`: front-right, slightly far (approx 4-8 units), on front wall. Let's place it at (3, 4) on the North wall of Room 1.
3. **Action**: Jump to `blue door`. Rotate 180 (face S).
* Agent is now at `blue door` (approx 3, 4), facing South.
4. **Observation 2 (from blue door facing S)**:
* `television`: front-right (SW from door), slightly far. Door is at (3,4), facing S. Front is S, Right is W. So SW direction. Approx (0, 0) or similar. Facing Left (East).
* `cap`: front-slight-right (S/SW), slightly far. Facing Left (East).
* `green door`: front-left (SE from door), mid distance. Facing S, Left is E. So SE direction. Mid dist (~3 units). Let's estimate (6, 1). On "left wall" (East wall relative to S facing agent).
* Constraint: `television` is East, near to `cap`.
5. **Action**: Rotate 180 (face N). View into Room 2.
* Agent at `blue door` (3, 4), facing North.
6. **Observation 3 (from blue door facing N)**:
* `vase`: front-left (NW), slightly far.
* `rubberduck`: front-slight-left (NNW), slightly far. Facing Left (West).
7. **Action**: Jump to `vase`. Rotate 180 (face S).
* Jump from (3,4) to `vase` (approx -1, 8 or similar). Facing S.
8. **Observation 4 (from vase facing S)**:
* `chair`: front-left (SE from vase), slightly far. Facing Left (East).
* `backpack`: front (S from vase), near. Facing Forward (South).
* `blue door`: front-left (SE from vase), slightly far. Confirms vase is NW of door.
9. **Action**: Jump to `blue door` (3, 4). Jump to `green door` (approx 6, 1). Rotate -90 (face E).
* Agent at `green door` (6, 1), facing East (into Room 3).
10. **Observation 5 (from green door facing E)**:
* `truck`: front-right (SE), slightly far. Facing Backward (West).
* `pan`: front-right (SE), mid distance. Facing Forward (East).
* `shelf`: front-right (SE), slightly far.
* Constraint: `truck` is North, near to `pan`.
11. **Action**: Jump to `pan`. Rotate -90 (face N).
* Agent is now at `pan` (approx 8, -1), facing North.
12. **Observation 6 (from pan facing N)**:
* `green door`: front-left (NW), mid distance. Confirms pan is SE of green door.

**Coordinate Estimation**:
* **Room 1**:
* Agent Start: (0,0).
* `lamp`: (0, 3) (Front mid).
* `bike`: (2, 2) (Front-right mid). Facing West.
* `blue door`: (2, 4). (Front-right slightly far). Let's adjust to fit grid. Maybe (3, 4) or (2, 5). Let's use (2, 5) as the wall.
* `green door`: From `blue door` (facing S), it was front-left (SE). If blue door is (2, 5), S is down. Left is East. So SE is correct. Distance mid (~3). Position: (5, 2).
* `television`: From `blue door` (facing S), front-right (SW). Start (0,0) is SW. Let's put TV near (0,0). Facing East.
* `cap`: Near TV.
* **Room 2** (North of Room 1):
* Connects at `blue door` (2, 5).
* `vase`: From door (facing N), front-left (NW). Slightly far (~5). Position: (-1, 8).
* `rubberduck`: Front-slight-left (N/NW). Position: (1, 9). Facing West.
* `chair`: From vase (facing S), front-left (SE). Slightly far. Position: (3, 6). Facing East.
* `backpack`: From vase (facing S), front (S). Near. Position: (-1, 6). Facing South.
* **Room 3** (East of Room 1):
* Connects at `green door` (5, 2).
* Agent at door facing E.
* `pan`: Front-right (SE). Mid dist (~3). Position: (7, 0). Facing East.
* `truck`: North of pan. Position: (7, 1). Facing West.
* `shelf`: Near/SE. Position: (8, 0).
* `laptop`: Not seen yet? Wait, list had laptop. I haven't seen laptop yet. Ah, I missed it? Re-reading observations.
* Obs 1: bike, lamp, blue door.
* Obs 2: television, cap, green door.
* Obs 3: vase, rubberduck.
* Obs 4: chair, backpack, blue door.
* Obs 5: truck, pan, shelf.
* Obs 6: green door.
* I have not seen `laptop`. Is it in Room 3? Maybe obscured or I just haven't looked in the right direction. The list of objects in the prompt included `laptop`. I must have missed it or it wasn't in the FOVs. Wait, prompt says "Objects: 1: television... 12: laptop". I have seen 11 objects (including doors).
* Wait, I need to output observed objects. Laptop is not observed.
* Let's refine coordinates.
* Origin (0,0).
* `lamp`: (0, 3).
* `bike`: (2, 2) facing west.
* `blue door`: (3, 4).
* `green door`: (6, 1).
* `television`: (1, 1) facing east.
* `cap`: (1, 2) facing east.
* `vase`: (0, 8).
* `rubberduck`: (1, 8) facing west.
* `chair`: (4, 7) facing east.
* `backpack`: (0, 7) facing south.
* `pan`: (8, -1) facing east.
* `truck`: (8, 0) facing west.
* `shelf`: (9, -1).
* Agent is at `pan` (8, -1) facing North.

* Let's check the constraint "television is east, near to cap". If Cap is (1,2) and TV is (1,1), TV is south of Cap. If TV is East of Cap... Cap at (0, 1), TV at (1, 1). Let's adjust.
* From blue door (3,4) facing S: Cap is Front-Right (SW). TV is Front-Right (SW).
* Let's say Blue Door is (3,4).
* Green Door is (6,1). (SE of Blue Door).
* TV/Cap area: (1,1).
* Constraint: "television is east, near to cap".
* Cap at (0, 1). TV at (1, 1). This fits "TV is East of Cap".
* Coordinates:
* Agent: [8, -1], facing: "north"
* blue door: [3, 4]
* green door: [6, 1]
* lamp: [0, 3]
* bike: [2, 2], facing: "west"
* television: [1, 1], facing: "east"
* cap: [0, 1], facing: "east" (Wait, obs said facing left when I was facing S -> East. Correct).
* vase: [0, 8]
* rubberduck: [1, 9], facing: "west"
* chair: [4, 7], facing: "east"
* backpack: [0, 7], facing: "south"
* pan: [8, -1], facing: "east"
* truck: [8, 0], facing: "west"
* shelf: [9, -1]

* Refining relative positions.
* Pan is at (8, -1). Truck is North of Pan -> (8, 0).
* Shelf is front-right from door (6,1) facing E. Door->SE is (8, -1). If pan is (8, -1), shelf is near there.
* Agent is at pan.

FINAL ANSWER:
```json
{
"agent": {"position": [8, -1], "facing": "north"},
"blue door": {"position": [3, 4]},
"green door": {"position": [6, 1]},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"television": {"position": [1, 1], "facing": "east"},
"cap": {"position": [0, 1], "facing": "east"},
"vase": {"position": [0, 8]},
"rubberduck": {"position": [1, 9], "facing": "west"},
"chair": {"position": [4, 7], "facing": "east"},
"backpack": {"position": [0, 7], "facing": "south"},
"pan": {"position": [8, -1], "facing": "east"},
"truck": {"position": [8, 0], "facing": "west"},
"shelf": {"position": [9, -1]}
}
```

THINK:
I need to construct a global map based on the observations.
1. **Initial State**: Agent at (0,0), facing North (Room 1).
2. **Observation 1 (from 0,0 facing N)**:
* `bike`: front-right (NE), mid distance (approx 2-4 units). Let's estimate (2, 2) facing West (left).
* `lamp`: fro...

{
  "agent": {
    "position": [
      8,
      -1
    ],
    "facing": "north"
  },
  "blue door": {
    "position": [
      3,
      4
    ]
  },
  "green door": {
    "position": [
      6,
      1
    ]
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "television": {
    "position": [
      1,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      0,
      1
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      8
    ]
  },
  "rubberduck": {
    "position": [
      1,
      9
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      4,
      7
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      0,
      7
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      8,
      0
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      9,
      -1
    ]
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "north"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "north"
  }
}

THINK:
I am currently at the position of the "pan". My previous global orientation was East, and I rotated -90 degrees, so I am now facing **North**.
My current FOV is to the North.
I observed the "green door" to my front-left, mid distance, on the left wall.
In my local frame (agent is origin, +y is North):
- "green door": "front-left" means x < 0, y > 0. "mid distance" is (2, 4]. "on left wall" implies the wall is to my left (West), so the door likely faces East (+x relative to wall, or towards me).
Let's estimate coordinates. "front-left" is usually around -45 degrees. "mid distance" approx 3.
So position roughly [-2, 2] or [-3, 3]. Let's say [-2, 2].
The door is on the "left wall" (West wall of the room).
Relative to me (facing North), the door is to the West. The door connects Room 3 (where I am) to Room 1. Since I entered from Room 1 (facing East), the door is indeed on the West wall of Room 3.
The prompt asks for the local map of observed objects. Only the green door is reported in the last observation.

Observation parsing:
- `green door`: front-left, mid distance.
- Direction: Front-left (approx -45 deg relative to agent facing North).
- Distance: Mid (approx 3 units).
- Position estimate: x ≈ -2, y ≈ 2.
- "on left wall": Since I am facing North, the left wall is the West wall. The door is part of the wall. Doors usually face into the room or are perpendicular. If it's on the left wall, it faces East (+x in global, +x in local relative to agent facing N). But strictly, the door *object* orientation isn't always given as a facing direction like furniture. However, "on left wall" is the orientation info. I will just list position. If I must provide facing, doors on West wall face East. In local frame (facing N), East is +x.

Wait, looking back at previous turns to ensure I didn't miss anything in *current* FOV.
I just performed `Observe()`. The output was *only* the green door.
The "truck" and "shelf" were seen in the previous turn (from the door facing East). Now I am at the pan facing North. The truck was "front-right" from the door. The pan was "front-right" from the door.
If I am at the pan facing North, where is the truck?
From door (0,0 relative to door): Pan is at (x, -y) or (x, y)?
Door facing East.
Pan: front-right. Front=East, Right=South. So Pan is South-East of door.
Truck: front-right. Truck is South-East of door.
Constraint: "truck is north, near to pan."
If truck is North of pan, and I am at pan facing North, the truck should be in front of me?
However, the latest Observe() *only* reported the green door.
This implies the truck and shelf are NOT in the current FOV (90 degrees centered on North).
This means they are either behind me, to my far right/left, or blocked (unlikely given simple physics here).
If truck is North of pan, it should be at +y in local frame. Why wasn't it seen?
Maybe "near" distance is very small and it's considered "at" the same location or just slightly off?
Or maybe my coordinate inference is slightly off.
Let's re-read: "truck is north, near to pan."
If I am at pan facing North, "Truck is North" means it is directly in front of me.
Why did `Observe()` not report it?
Possibility 1: It is not in FOV. (Maybe it's actually North-West or North-East and outside the cone?)
Possibility 2: The system only reports *new* things? No, the rules say "Report objects ... in your FOV".
Possibility 3: "Truck is North of pan" is a relative statement provided *after* the previous observation. "Assume your current facing direction is called 'north': truck is north, near to pan."
Wait, that relative statement was given when I was at the *green door* facing *East*.
At green door, facing East (call it "north" for the relative clue):
"truck is north [East in reality], near to pan."
This is confusing. Let's parse strictly.
Turn 4 (at green door, facing East): "Assume your current facing direction [East] is called 'north': truck is north [East], near to pan."
So Truck is East of Pan.
Now (Turn 5): I am at Pan. I face North (Global North).
Truck is East of Pan.
My FOV is North (Global).
East is to my Right (Global).
Right is 90 degrees relative to my facing.
The FOV is 90 degrees (45 left to 45 right).
East is 90 degrees right. It is *outside* the FOV (which ends at 45 right).
This explains why I don't see the truck.
So, the only object in FOV is the green door.

Object: Green Door.
Position: Front-left.
Approx coordinates relative to agent (facing N): x negative, y positive.
Distance "mid" (2 to 4). Let's use x=-2, y=2.
Facing: "on left wall". Agent faces N. Left wall is West. Door faces East (+x).

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"green door": {"position": [-2, 2], "facing": "+x"}
}
}

THINK:
I am currently at the position of the "pan". My previous global orientation was East, and I rotated -90 degrees, so I am now facing **North**.
My current FOV is to the North.
I observed the "green door" to my front-left, mid distance, on the left wall.
In my local frame (agent is origin, +y i...

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        -2,
        2
      ],
      "facing": "+x"
    }
  }
}

{
  "green door": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        -2,
        2
      ],
      "facing": "+x"
    }
  }
}

THINK:
I need to identify which candidate points (A-F) lie in unexplored or unobserved regions based on my current location and previous observations.

1. **Current State**:
* I am in **Room 3**.
* I am standing at the `pan`.
* I just rotated to face **North**.
* My observation shows the `green door` is to my front-left (North-West) on the left wall.

2. **Room 3 Layout & Observations**:
* **Entry**: I entered Room 3 via the `green door` (located on the East wall of Room 1, so the West wall of Room 3).
* **Initial View (from Green Door facing East)**:
* `truck`: front-right (South-East).
* `pan`: front-right (South-East). I am here now.
* `shelf`: front-right (South-East).
* **Current View (from Pan facing North)**:
* `green door`: front-left. This confirms the door is North-West of me.
* I am looking North. My field of view (90°) covers North-West to North-East.
* I see the `green door` (North-West).
* I do *not* see any other objects listed in the current observation, implying the area directly North and North-East is empty or contains no *previously seen* objects (except the door). However, the task asks for *unobserved* regions.

3. **Analyzing Candidates**:
* The map shows Room 3 as the bottom-right room.
* The `green door` (`+`) connects the left room (Room 1) to Room 3.
* My position (`*`) is in the middle-ish of Room 3.
* **Candidate A**: Located to the East of me, slightly South. From the door (facing East), this area (front-right/far right) was likely covered by the "front-right" observation of the truck/shelf. From my current position (facing North), this is to my **Right (East)**. My FOV is North (NW to NE). "Right" (East) is **outside** my current FOV. While the initial view from the door might have caught it, the query implies checking what is currently unexplored/ambiguous or simply confirming coverage. Usually, "front-right" from the door covers the SE corner. Let's look closer. From the door, I saw truck/pan/shelf in "front-right". A is in that cluster. However, F, B, C, E are also there.
* **Candidate F**: West of me. From current facing (North), West is "Left". The door is "front-left". F is directly Left. This is likely on the edge of the FOV or just outside (Start of FOV is -45 deg, Left is -90). From the door (facing East), F would have been "Front". I saw nothing "Front", only "Front-Right". This suggests the area directly East of the door (F) might be empty or unobserved if the objects were all tucked in the corner.
* **Candidate D**: North-East of me. I am facing North. This is in my "Front-Right" sector. I currently see *nothing* there (observation only listed the door). This implies I have observed it and it is empty.
* **Candidates B, C, E**: South of me. I am facing North. This is "Behind" me. I have never looked South while in this room.
* From the door (facing East), I looked generally East. The "front-right" sector covers South-East. Objects truck/shelf were there.
* However, looking "Front-Right" from the door usually implies a cone. The deep South corners might be occluded or just "far".
* Critically, I have never stood at the Pan and looked South.
* Let's check the map coordinates visually.
* `*` (Pan) is at roughly x=10, y=4 (relative to room bottom-left).
* `D` is at x=12, y=5. (North-East). In current FOV. Observed (empty).
* `A` is at x=13, y=3. (South-East). Behind/Right of current FOV.
* `B`, `C` are at x=10/11, y=1. (South). Directly behind.
* `E` is at x=13, y=1. (South-East corner). Behind.
* `F` is at x=8, y=3. (West). Left.
* **Coverage History**:
1. **From Door (Facing East)**: Saw Truck, Pan, Shelf (all "Front-Right"). This covers the SE quadrant roughly.
2. **From Pan (Facing North)**: Seeing Green Door ("Front-Left"). Covers NW/N/NE.
* **Gaps**:
* I have not explicitly looked **South** or **West** from inside the room.
* The area directly East of the door (Candidate F) was "Front" from the door, but I only reported objects in "Front-Right". If F is empty space, it's observed-empty.
* The candidates A, B, C, E are in the South/South-East. While "Front-Right" from the door caught the *objects*, the *area* strictly South of the Pan might have parts not fully resolved, specifically behind the Pan relative to the door? No, from the door, Pan is in front. Behind the Pan (from the door's perspective) is further East.
* However, from the Pan's perspective, I am facing North. Everything behind me (South) is currently unobserved *from this vantage point*. But the Fog Probe asks for "unexplored/unobserved regions" of the map generally.
* Did the view from the door cover B, C, E? "Front-Right" is a cone 0 to -90 (East to South). If I am at the West wall facing East, Front-Right covers the South-East room.
* However, candidate **D** is North-East. I am facing North now, so I see it.
* Candidate **F** is West (Left). From the door, it was Front.
* The candidates that are most likely "unexplored" in a rigorous sense (often meaning 'behind obstacles' or 'outside FOV cones') are those in the South if the initial view was narrow, or corners.
* Let's look at the symbols. The previous turn I was at the green door facing East. I saw truck, pan, shelf "front-right".
* Now I am at Pan (which was front-right). Facing North.
* I have seen the SE corner (from the door). I am seeing the N/NW sector (from Pan).
* What about the SW corner? Or the area directly South of the Pan?
* B, C, E are South. F is West. A is East.
* Usually, single observations don't clear the whole room in these logic puzzles if the FOV is strict 90 degrees.
* From Door (Facing East): FOV is NE to SE. (Left=N, Right=S). Wait.
* Agent Facing: East (0° relative to agent).
* FOV: -45° to +45°? No, "FOV is 90°". Usually [-45, 45].
* If FOV is [-45, 45] relative to facing:
* Facing East. FOV covers North-East to South-East?
* Standard: North (0). Right (90)=East. Left (-90)=West.
* Agent Facing East. Front=East.
* FOV [-45, 45] around East = [North-East, South-East].
* So from the door, I saw everything in the cone towards the East wall.
* Candidates A, B, C, D, E, F are all technically "East" of the door.
* However, B, C, E are deep South. If the room is wide, they might be outside the [-45] cone (which would be South-East). If they are strictly South of the door-pan line, they might be missed?
* F is x=8, Door is x=6?. F is near the center-line. Likely observed.
* A, B, C, E are in the South-East corner. Likely observed by "Front-Right" (SE).
* **Wait**, look at the map. The map shows the Agent (*) at x=~10. The Door (+) is at x=~6.
* F is between Door and Agent.
* D is North of Agent.
* A is East of Agent.
* B, C, E are South of Agent.
* **The crucial part**: The Fog Probe often highlights areas the agent *has not effectively cleared*.
* I have looked East (from door) and North (from Pan).
* I have **never** looked South (from Pan) or West (from Pan, looking back at F).
* From the door, F was "Front". D was "Front-Left" (NE). A was "Front". B/C/E were "Front-Right" (SE).
* My observation from the door only reported "truck, pan, shelf" in "front-right".
* This implies I did **not** see objects in "Front" (East) or "Front-Left" (NE).
* If F and A were in "Front" and I reported nothing, they are empty.
* If D was in "Front-Left" and I reported nothing, it is empty.
* If B/C/E were in "Front-Right" and I reported objects, they contain objects (or are near them).
* However, usually, if I haven't visited or "Observed" a specific cone from a closer vantage, it might be marked.
* Let's reconsider the "Unexplored" definition. It usually means grid cells that have not fallen within the FOV cone of any `Observe` action.
* Action 1 (Room 3): At Green Door (West wall), facing East.
* Cone: North-East (-45) to South-East (+45).
* This cone covers the center and right wall.
* It likely misses the **corners** on the wall I'm standing on (North-West and South-West corners of Room 3).
* It also misses the deep South and deep North if the room is wide and short.
* Action 2 (Room 3): At Pan (Center), facing North.
* Cone: North-West to North-East.
* This covers the area "above" the Pan.
* **D** is in this cone.
* **What is missed?**
* **South of the Pan**: The cone from the door (facing East) covered the vector towards the Pan. Did it cover the area *below* (South of) the Pan?
* If the Pan is at angle 0 (East), the cone goes down to -45 (South-East). B, C, E are likely in this cone.
* **West of the Pan (behind me now)**: F. From the door, looking East, F is in the line of sight.
* **The Logic Trap**: The problem often implies that if you jump to an object, you haven't necessarily "scanned" the area around it, only the path? No, "Observe" scans the FOV.
* Let's look at the candidates again.
* D: North-East. Covered by current view (Facing N).
* F: West. Covered by Door view (Facing E).
* A: East. Covered by Door view (Facing E).
* B, C, E: South. Covered by Door view (Facing E) *if* they fall in the SE cone.
* However, looking at the layout: The door is at y=8ish. The pan is at y=4ish. This is a sharp angle.
* Door (x=6, y=8). Pan (x=10, y=4). Vector = (4, -4). Angle = -45 degrees (South-East).
* If I face East (0 degrees), the Pan is at -45 degrees. This is at the very edge of the FOV (Right boundary).
* Objects *further South* than the Pan (B, C, E are at y=1) would have an angle *steeper* than -45 degrees (e.g., dx=4, dy=-7 -> angle ~ -60).
* **These objects (B, C, E) would be OUTSIDE the FOV of the first observation.** (Since FOV is max 45 degrees to the right).
* Therefore, **B, C, E** are definitely unexplored.
* What about **A**? x=13, y=3. Vector from door (6,8) -> (7, -5). Angle ~ -35 degrees. Inside FOV.
* What about **F**? x=8, y=3. Vector from door (6,8) -> (2, -5). Angle ~ -68 degrees. Outside FOV (Too far South/Right).
* Wait, is F at y=3?
* Map:
* `*` is at row 5 (counting up from bottom). Let's trace.
* Row 15: ####...
* ...
* Row 8: ######+####### (Door at x=7)
* ...
* Row 4: #......#.*..D.# (Pan at x=10?)
* Let's count dots from left wall # (x=0).
* Row 4: # (1) . . . . . . # (8) . * (10) . . D (13) . #
* Agent * is at x=10 relative to the map grid.
* Door + is at Row 8, Col 7.
* Coordinates Check:
* Door: (7, 8)
* Pan (*): (10, 4)
* Vector: (3, -4). Angle: atan(-4/3) = -53 degrees.
* If I faced East (0), the Pan itself was at -53 degrees.
* **This is OUTSIDE the standard 45 degree FOV.**
* How did I see the Pan?
* Maybe "Front-Right" implies I was facing East, but the bin "Front-Right" captures (22.5, 45]? Or maybe the bins go wider?
* Instruction: "Egocentric angle bins ... (22.5°,45°]→front-right, otherwise→beyond-fov."
* Strictly, if Pan is at -53, it is "beyond-fov".
* However, I *did* see it.
* Possibility 1: I was not facing strictly East (0).
* Possibility 2: The door is not at (7,8) or Pan not at (10,4).
* Possibility 3: "Front-Right" bin extends further? No, rules say "otherwise -> beyond-fov".
* Maybe the door is lower? Or Pan higher?
* Let's count again.
* Row 1: ######## . B C . E . #
* Row 2: #......# F ... A . #
* Row 3: #......#......#
* Row 4: #......#.*..D.#
* Row 8: Door.
* Gap is 4 rows.
* Horizontal gap is 3 cols.
* Angle is definitely steep.
* Perhaps I entered and faced *South-East*? No, action was `JumpTo(green door)`. Orientation matches door? Usually door orientation is normal to wall. Green door on Left wall (East wall of Room 1) -> Faces East.
* Maybe the map grid is just illustrative and not precise to the text description?
* Text says: "truck: front-right... pan: front-right...".
* If I saw them, they are in FOV.
* However, **B, C, E** are even *more* South than the Pan. If Pan was barely in (or I'm miscalculating), B/C/E are likely out.
* **F** is at y=3 (Row 2 in my count, actually Row 3 in 1-based?).
* Let's assume the text observation is truth. Pan is visible.
* Areas *South* of Pan (B, C, E) are at a sharper angle. Likely unobserved.
* Areas *West* of Pan (F) are "Left" of the Pan vector. From Door, F (x=8, y=3) vs Pan (x=10, y=4).
* Vector to F: (1, -5). Angle -78. Definitely Out.
* So F is unobserved.
* **D** (x=12, y=4). Vector (5, -4). Angle -38. In FOV. Observed. Also in current FOV (Facing N).
* **A** (x=13, y=3). Vector (6, -5). Angle -40. In FOV? Borderline.
* **B, C** (x=10, 11, y=1). Vector (3, -7). Out.
* **E** (x=13, y=1). Vector (6, -7). Out.

* **Conclusion**:
* Candidates deep in the South (B, C, E) and West-South (F) were too steep to see from the door (facing East) and are behind me now (facing North).
* **A** is borderline, but likely observed from door or obscured. Given it's "behind" the current facing and low down, I'll include it to be safe, or exclude if I trust the door view covered -40 deg.
* Usually, these fog maps want the *clearly* missed areas.
* F is definitely missed (steep angle).
* B, C, E are definitely missed (steep angle).
* A is likely seen (Angle -40 is < 45).
* D is seen.
* So: B, C, E, F.
* Let's check A again. If I see truck/pan/shelf, and A is near them? Truck usually implies "large".
* Let's stick to the geometry. Steep angles = Missed.
* F, B, C, E.

* Refined list: B, C, E, F.

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

THINK:
I need to identify which candidate points (A-F) lie in unexplored or unobserved regions based on my current location and previous observations.

1. **Current State**:
* I am in **Room 3**.
* I am standing at the `pan`.
* I just rotated to face **North**.
* My observat...

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#......+......#
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#......#.*..D.#
#......#......#
#......#F...A.#
########.BC.E.#
###############

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

I am at the 'pan' in Room 3, facing North.
I have observed the 'green door' to my front-left (West wall).
I previously saw a 'truck' and 'shelf' from the door.
I need to check if I have missed any objects.
From the door (facing East), I saw truck, pan, shelf to the front-right.
Now at the pan (facing North), I see the green door.
I haven't explicitly observed the 'truck' or 'shelf' from *this* position, but they were near the pan.
I might have missed objects in the South-East or South-West corners of Room 3, which are now behind me or to my right.
However, the goal is to terminate once the map is complete.
I have visited:
Room 1: blue door, lamp, bike, television, cap, green door.
Room 2: vase, rubberduck, chair, backpack.
Room 3: truck, pan, shelf.
I have identified 12 objects:
1: television (Room 1)
2: chair (Room 2)
3: truck (Room 3)
4: bike (Room 1)
5: backpack (Room 2)
6: pan (Room 3)
7: cap (Room 1)
8: lamp (Room 1)
9: vase (Room 2)
10: shelf (Room 3)
11: rubberduck (Room 2)
12: laptop (NOT FOUND YET)
I am missing the 'laptop'.
I need to find the laptop. It wasn't seen in Room 1 (fully mapped?), Room 2 (fully mapped?), or the initial view of Room 3.
In Room 3, from the door (facing East), I saw truck/pan/shelf to the right. I did not see the "left" (North) part of Room 3 clearly, or maybe it was empty.
Now at 'pan' facing North, I only see the green door.
This implies the North part of Room 3 is empty or the laptop is hidden.
Wait, if I am at the pan facing North and see the door to the front-left, the area to my front (North) and front-right (East) is in my FOV. If the laptop were there, I would see it.
The only blind spots are:
1. Behind me (South). I am at the pan (which was "front-right" from the door). So I am South-ish. Behind me is the South wall.
2. To my right (East).
3. Room 1 or Room 2 corners I might have missed.
Let's re-evaluate Room 2. I jumped to 'vase', rotated 180 (facing South), saw chair, backpack, blue door. I did *not* see the North wall of Room 2 from the inside. When I stood at the blue door facing North, I saw vase and rubberduck. I might have missed something in the North-East or North-West corners of Room 2 if the FOV didn't catch it, or if it was occluded.
However, Room 3 seems less explored. I only had one view from the door (facing East) and one view from the pan (facing North).
From the door, I saw right (South).
From the pan (South), I look North and see the door.
I haven't looked East or South from the pan.
Let's rotate to check the South/East corners of Room 3.
Rotate 90 (to face East) or 180 (to face South).
If I rotate 180 (face South), I look at the wall behind the pan.
If I rotate 90 (face East), I look deeper into the room (if it's wide).
Let's try Rotate(90) to face East. This covers the remaining sector of Room 3.
If I don't find it there, I might have to go back to Room 1 or 2.
Wait, I saw "laptop" in the list of objects in the prompt? Yes, object 12.
I must find it.
Let's search Room 3 thoroughly first.
Action: Rotate 90 (face East) and Observe.

I am at the 'pan' in Room 3, facing North.
I have observed the 'green door' to my front-left (West wall).
I previously saw a 'truck' and 'shelf' from the door.
I need to check if I have missed any objects.
From the door (facing East), I saw truck, pan, shelf to the front-right.
Now at the pan (facin...

THINK:
I need to construct the JSON map based on my observations.
Initial state: (0,0), facing North (Room 1).
Observed from (0,0) facing North:
- lamp: front, mid distance (~3 units North). Pos: (0, 3).
- bike: front-right, mid distance (~3 units distance, angle ~45 deg). Pos: (2, 2) or (2, 3). Facing Left (West).
- blue door: front-right, slightly far, on front wall. "Slightly far" is (4,8]. Let's estimate (0, 6) or similar for the wall. Door is on front wall (North wall).

Step 1: Jumped to blue door. Rotated 180 (facing South).
- From blue door facing South:
- television: front-right (West-ish), slightly far. Facing Left (East? No, facing "left" relative to me facing South means facing East).
- cap: front-slight-right, slightly far. Facing Left.
- green door: front-left (East wall), mid distance.
- Relation: television is east, near to cap. This contradicts "television front-right" (West) if I am facing South.
Wait, if I am facing South:
Front = South.
Right = West.
Left = East.
Observed: television: front-right (South-West).
Observed: cap: front-slight-right (South, slightly West).
Observed: green door: front-left (South-East). On left wall (East wall).
Constraints say: "television is east, near to cap".
If Cap is at (x_c, y_c) and TV is East of it, TV has larger x.
My observation says TV is front-right (West side) and Cap is front-slight-right (West side).
If TV is to the *right* of Cap (from my perspective facing South), that means TV is further West.
But the constraint says "television is east... to cap". This is a contradiction or I misunderstood the "facing" relative description.
Let's re-read: "Assume your current facing direction is called 'north': television is east, near to cap."
My current facing is South. So in the "relative frame" where South is North:
East relative to "relative North" is East relative to South, which is *Left* (global East).
So TV is to the left (East) of Cap in the global frame?
No, "Assume your current facing direction (South) is called 'north'".
Then "television is east (relative)" means to the right of the agent?
Standard cardinal: N, E, S, W.
If Agent Face = South.
Relative North = South.
Relative East = East (90 deg clockwise from N). If N=South, E=West.
So "television is east" means "television is to the West (global)".
This matches "front-right" (global South-West).
Okay, so TV is West of Cap.
Coordinates estimation:
Blue door at (0, 6) approx.
Agent at (0, 6) facing South.
Green door: front-left (South-East). Wall is East. Let's say x=4?
TV: front-right (South-West). x < 0.
Cap: front-slight-right. x slightly < 0.

Step 2: Rotated 180 (facing North). Now at blue door facing North (into Room 2).
- vase: front-left (North-West), slightly far.
- rubberduck: front-slight-left (North-West), slightly far. Facing Left (West).

Step 3: Jumped to vase. Rotated 180 (facing South).
- chair: front-left (South-East relative to vase), slightly far. Facing Left (East).
- backpack: front (South), near. Facing Forward (South).
- blue door: front-left (South-East relative to vase), slightly far. On front wall (South wall of Room 2).
This confirms vase is North-West of the blue door.

Step 4: Jumped to blue door, then green door.
Green door is on East wall of Room 1.
Agent at green door facing South? No, previous step I jumped to green door.
My orientation didn't change during JumpTo. I was at vase facing South. Jump to blue door (facing South). Jump to green door (facing South).
Then Rotated -90 (Left). Now facing East (into Room 3).
Observed:
- truck: front-right (South-East), slightly far. Facing backward (West).
- pan: front-right (South-East), mid distance. Facing forward (East).
- shelf: front-right (South-East), slightly far.
Relation: "Assume current facing (East) is North".
"Truck is north, near to pan."
Relative North = East. Relative East = South.
"Truck is north" means Truck is further East than Pan? Or in the "North" direction relative to the frame.
If Frame N = Global E. Then Relative N is Global E.
So Truck is East of Pan.
Observation says both are front-right (South-East).

Step 5: Jumped to pan. Rotated -90 (facing North).
- green door: front-left (North-West), mid distance. On left wall (West wall).
This confirms Pan is South-East of the Green Door.

Step 6: Rotated 90 (facing East).
- truck: front (East), near. Facing backward (West).
- shelf: front-right (South-East), slightly far.

We still haven't found the laptop.
I have explored:
Room 1 (South of blue door, West of green door).
Room 2 (North of blue door).
Room 3 (East of green door).
Objects found:
Room 1: Lamp, Bike, TV, Cap. (4 objects)
Room 2: Vase, Rubberduck, Chair, Backpack. (4 objects)
Room 3: Truck, Pan, Shelf. (3 objects)
Total 11 objects. Laptop is missing.
Possible locations:
Room 1: I saw front, front-right from start. Then from door (facing S), saw TV/Cap (Right/West) and Green Door (Left/East). I didn't explicitly see the "front-left" (South-East) corner of Room 1 from the blue door, nor the "front-left" (North-West) from start.
Wait, from start (facing N):
- Lamp (Front)
- Bike (Front-Right)
- Blue Door (Front-Right, on Front Wall)
I did not see anything Front-Left (North-West).
From blue door (facing S):
- TV (Front-Right -> South-West)
- Cap (Front-Slight-Right -> South-West)
- Green Door (Front-Left -> South-East)
I did not see anything Front-Left (South-East) other than the door.
Is there a corner in Room 1 I missed?
Maybe "North-West" corner of Room 1?
From start (0,0), facing N, I see [-45, 45]. West is outside FOV. North-West is outside FOV.
From blue door (facing S), I see [-45, 45] relative to South (i.e., South-East to South-West). North-West is behind me.
So the North-West corner of Room 1 has not been observed.

Room 2:
From blue door (facing N): Vase, Duck (Front-Left -> North-West).
From Vase (facing S): Chair (Front-Left -> South-East), Backpack (Front -> South), Blue Door (Front-Left).
I missed the North-East corner of Room 2.
From blue door (facing N), I saw Front-Left. Did I see Front-Right? No report.
From Vase (facing S), I see South-East.
So North-East of Room 2 is a candidate.

Room 3:
From Green Door (facing E): Truck, Pan, Shelf (Front-Right -> South-East).
From Pan (facing N): Green Door (Front-Left -> North-West).
From Pan (facing E): Truck (Front), Shelf (Front-Right -> South-East).
I haven't seen the North-East sector of Room 3.
From Pan (facing N), I see [-45, 45] relative to North. That covers North-West to North-East.
But I only reported Green Door (Front-Left). If there was something North-East, I should have seen it? Or maybe it was occluded or empty.
From Pan (facing E), I see East.
The "North" part of Room 3 (left of the door) might be empty.
But I suspect the missing laptop is in one of the unvisited corners: NW of Room 1, NE of Room 2, or somewhere in Room 3.
Given Room 3 had "Truck is north, near to pan" relative to East facing (so Truck is East of Pan), and I found Truck East of Pan (Step 6), that's consistent.

Let's hypothesize coordinates to build the map.
Start (0,0).
Blue door: (0, 5) ?
Lamp: (0, 3).
Bike: (2, 2).
Room 1 width: maybe -3 to 3?
Green door: on Left wall (East wall) from blue door facing S?
Wait, from blue door (facing S), Green door is Front-Left. Front is S. Left is E. So Green door is South-East of Blue door.
Blue door at (0, 6) on N wall.
Green door at (4, 3) on E wall?
Room 3 is East of Green door.
Room 2 is North of Blue door.

Let's refine coordinates.
Room 1:
Agent Start (0,0).
Lamp (0, 2) [Mid dist 2-4].
Bike (2, 2) [Mid dist].
Blue Door (1, 5) ? "Front-Right". "Slightly far" (4-8). Say (1, 6).
From Blue Door (1, 6) facing S:
TV (Front-Right). S is Front. Right is W. So South-West of (1,6). Say (-2, 2). "Slightly far".
Cap (Front-Slight-Right). Say (0, 3). "Slightly far".
Green Door (Front-Left). South-East of (1,6). Say (5, 3). "Mid dist" (2-4). Distance sqrt(4^2 + 3^2) = 5 (slightly far). Distance bins are loose.
Let's assume Green Door is at (5, 2).

Room 2:
From Blue Door (1, 6) facing N:
Vase (Front-Left). North-West. Say (-2, 9). "Slightly far".
Rubberduck (Front-Slight-Left). Say (0, 9). "Slightly far".
From Vase (-2, 9) facing S:
Chair (Front-Left). South-East. Say (1, 7). "Slightly far".
Backpack (Front). South. Say (-2, 8). "Near" (0-2).
Blue door is at (1, 6). From (-2, 9), (1, 6) is dx=3, dy=-3. South-East. "Front-Left". Matches.

Room 3:
Green Door at (5, 2).
Agent at (5, 2) facing E.
Truck (Front-Right). South-East. Say (8, 0). "Slightly far".
Pan (Front-Right). South-East. Say (7, 1). "Mid distance".
Shelf (Front-Right). South-East. Say (8, -1).
From Pan (7, 1) facing N:
Green Door (5, 2) is dx=-2, dy=1. North-West. "Front-Left". Matches.
From Pan (7, 1) facing E:
Truck at (8, 1)? "Front, near". (8, 1) is East of (7, 1). Distance 1. Matches "Near".
Shelf at (8, 0)? "Front-Right". South-East. Matches.

So Laptop is likely in Room 1 NW corner or Room 2 NE corner.
I have 14 steps left.
I am at Pan (7, 1) facing East.
I need to go back to Room 1 or Room 2.
Route: Pan -> Green Door -> Room 1 -> Blue Door -> Room 2?
Let's check Room 1 NW corner first.
JumpTo(Green Door). Facing E? No, facing E from last rotation?
I am at Pan facing E.
JumpTo(Green Door).
From Green Door, I need to look at Room 1 NW corner.
Green door is at (5, 2) on East wall.
To see NW corner (e.g. -3, 6), I should be in Room 1.
I am at Green Door. Facing E?
Movement doesn't change orientation.
Pan facing E. Jump to Green Door. Facing E.
Green door is interface. I am now at interface.
To see Room 1, I should face West.
Rotate(180).
Now facing West into Room 1.
Observe. This might reveal the Laptop in NW corner.

Wait, I missed the "laptop" in the prompt object list?
"Objects: 1: television, ... 12: laptop".
Yes.
So I definitely need to find it.
My plan is to backtrack.
1. JumpTo(green door).
2. Rotate(180) to face West. Observe Room 1.
If not there:
3. JumpTo(blue door).
4. Rotate(180) to face North (or just observe if I can see NE corner from door).
From Blue Door facing N, I saw NW (Vase). I might not have seen NE.
So I might need to Rotate to see NE.

Let's start with Room 1.
Map update:
Agent at Pan (7, 1), facing East.

FINAL ANSWER:
```json
{
"agent": {"position": [7, 1], "facing": "east"},
"lamp": {"position": [0, 2], "facing": null},
"bike": {"position": [2, 2], "facing": "west"},
"blue door": {"position": [1, 6], "facing": "south"},
"television": {"position": [-2, 2], "facing": "east"},
"cap": {"position": [0, 3], "facing": "east"},
"green door": {"position": [5, 2], "facing": "west"},
"vase": {"position": [-2, 9], "facing": null},
"rubberduck": {"position": [0, 9], "facing": "west"},
"chair": {"position": [1, 7], "facing": "east"},
"backpack": {"position": [-2, 8], "facing": "south"},
"truck": {"position": [8, 1], "facing": "west"},
"pan": {"position": [7, 1], "facing": "east"},
"shelf": {"position": [8, 0], "facing": null}
}
```

THINK:
I need to construct the JSON map based on my observations.
Initial state: (0,0), facing North (Room 1).
Observed from (0,0) facing North:
- lamp: front, mid distance (~3 units North). Pos: (0, 3).
- bike: front-right, mid distance (~3 units distance, angle ~45 deg). Pos: (2, 2) or (2, 3). Fac...

{
  "agent": {
    "position": [
      7,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      2
    ],
    "facing": null
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      1,
      6
    ],
    "facing": "south"
  },
  "television": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      0,
      3
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      5,
      2
    ],
    "facing": "west"
  },
  "vase": {
    "position": [
      -2,
      9
    ],
    "facing": null
  },
  "rubberduck": {
    "position": [
      0,
      9
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      1,
      7
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -2,
      8
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      8,
      1
    ],
    "facing": "west"
  },
  "pan": {
    "position": [
      7,
      1
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      8,
      0
    ],
    "facing": null
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  }
}

THINK:
I am currently at the position of the 'pan' in Room 3.
I have just rotated 90 degrees clockwise from North, so I am now facing East.
My current observation is:
- `truck`: front, near, facing backward.
- `shelf`: front-right, slightly far.

Relative to my current position (origin) and facing (local +y):
- `truck`: "front" means roughly +y. "near" means distance (0, 2]. Let's estimate local position [0, 2]. Facing "backward" relative to me means it faces -y (towards me).
- `shelf`: "front-right" means roughly (+x, +y). "slightly far" means distance (4, 8]. Let's estimate local position [3, 4] or similar. No facing information given.

I need to construct the Local Cognitive Map based on these relative coordinates.
Constraints:
- Origin: "agent"
- Objects: truck, shelf.
- Coordinates: Integer approximations based on distance bins and angle bins.

Estimations:
Truck: Front (0°), Near (dist ~1-2). Let's say (0, 2). Facing: Backward relative to agent. Agent faces +y, so truck faces -y.
Shelf: Front-Right (~45°), Slightly Far (dist ~5-6). Let's say (4, 4). Facing: Not specified.

Wait, let's refine the "facing backward".
"facing backward" in the observation usually means the object's front is directed towards the agent's back? Or does it mean the object is facing the direction 'backward' relative to the agent's current frame?
Standard interpretation:
"facing left" -> faces agent's left (-x).
"facing backward" -> faces agent's back (-y).
So if I am facing East (Global), the truck is facing West (Global). In local frame (+y is forward), the truck faces -y.

Let's verify the previous observation of truck.
From door (facing East): truck was front-right, facing backward.
Agent was East. Truck was South-East. Facing backward (West?).
Now Agent is at Pan (South-East). Facing East. Truck is Front (East). Facing backward (West?).
This is consistent.

Let's build the JSON.

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"truck": {"position": [0, 2], "facing": "-y"},
"shelf": {"position": [4, 4]}
}
}

THINK:
I am currently at the position of the 'pan' in Room 3.
I have just rotated 90 degrees clockwise from North, so I am now facing East.
My current observation is:
- `truck`: front, near, facing backward.
- `shelf`: front-right, slightly far.

Relative to my current position (origin) and facing (...

{
  "origin": "agent",
  "objects": {
    "truck": {
      "position": [
        0,
        2
      ],
      "facing": "-y"
    },
    "shelf": {
      "position": [
        4,
        4
      ]
    }
  }
}

{
  "truck": {
    "position": [
      0,
      2
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      2,
      4
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "truck": {
      "position": [
        0,
        2
      ],
      "facing": "-y"
    },
    "shelf": {
      "position": [
        4,
        4
      ]
    }
  }
}

THINK:
I am currently in Room 3 (the rightmost room based on the map layout). My position is marked by `*`. I am facing East (Right).
I have observed the `truck` (front, near) and `shelf` (front-right, slightly far).
The `pan` (my previous location/jump target) is nearby.
The map shows Room 3 to be the area on the right.
Candidate points A, B, C, D, E, F are in Room 3.
I have observed from the door (facing East) and from the pan/current pos (facing North, and now East).
When facing North from `*`, I saw the green door (to the left/West).
When facing East from `*`, I see the truck (front) and shelf (front-right).
This covers the area to the East (Right) and South-East (Down-Right) of my position.
My previous view from the door covered the South-East area roughly.
My view North covered the area North of `*`.
Let's analyze the candidates:
`*` is my position.
`F` is to my North-West. When I faced North, I saw the Green Door to my front-left. `F` is likely in that cone or near it. However, `F` looks to be 'behind' the line of sight if I was at the door looking SE, and when I was at `*` looking North, `F` would be to my left/front-left. I saw the door there. `F` is between me and the door/wall. It's likely observed or empty floor. But is it "unexplored"? The question asks for points in "unexplored/unobserved regions".
`B` is in the far North-East corner. When facing North, I saw the door (North-West-ish). Did I see the North-East corner? My FOV is 90 degrees. Facing North, I see NW to NE. If `B` is far enough East, I might have missed it or it was on the periphery. However, when I entered and looked from the door (facing East), I saw "truck, pan, shelf" which are Central/South. I might not have seen the deep North-East corner.
`D` is to my East. I am currently facing East. I see truck and shelf. `D` is likely in my current FOV.
`A` and `C` are to the South/South-East. When facing East, `A` is front-right. I see the shelf there.
`E` is in the deep South-West corner. When I was at the door facing East, this was to my right. When I am at `*` facing East, this is to my right (outside FOV). When I was at `*` facing North, this was behind me. I haven't looked specifically at the South-West corner `E`.
`B` (North-East corner): When facing North, I saw the Green Door (West wall). I didn't report seeing the North or East walls. The view from the door (facing East) saw objects to the South-East. The North-East corner `B` is a strong candidate for being unobserved.
`E` (South-West corner): I haven't looked South or West from inside the room deep enough to see the corner `E` specifically.
`F` (North-West area): I saw the door there. It's likely observed space.

Refining "unexplored":
I am looking for the `laptop`.
I have looked North (saw door).
I am looking East (see truck, shelf).
I looked from Door to South-East (saw pan, truck, shelf).
I have NOT looked at the South-West corner (`E`) from inside.
I have NOT looked at the North-East corner (`B`) closely (facing North I saw door on left; did I see the right side? FOV is front-left to front-right. If door is front-left, front-right is the NE corner. But I reported *nothing* there. This suggests it's empty or I didn't see it).
However, the most likely unobserved areas are the corners I haven't faced directly.
`E` is behind/right of my current view and was right of my entry view.
`B` was possibly in my North view, but if it's far, maybe not fully resolved.
The candidates `A`, `C`, `D` are around the objects I see now (shelf/truck).
`F` is near the path from the door.

I will select `B` and `E` as the most likely unobserved/unexplored areas. `F` is also a possibility if my North view was focused on the door. But `B` and `E` are corners.
Let's check the coordinates. `*` is roughly (10, 3) relative to the room bottom-left? No, looking at the map ASCII:
The room is the block on the right.
`*` is somewhat central.
`B` is top right.
`E` is bottom left.
`A`, `C` are bottom right.
`D` is right.
`F` is top left.
Current view (East): Sees `D`, `A`, `C` (front and front-right).
Previous view (North): Saw Green Door (`+` on left). That covers `F` area? Door is at `y=8` approx? `F` is `y=4`?
Wait, if `*` is at `y=3` and door is `y=8` (based on visual rows), looking North sees `F`.
What about `B`? `B` is `y=6, x=13`. Facing North from `x=10, y=3`, `B` is front-right. It should be in FOV. If I saw nothing, it's empty.
What about `E`? `E` is `x=8, y=0`. `*` is `x=10, y=3`. `E` is South-West.
From door (x=6, y=7?), facing East. `E` is South-West. Behind/Right.
From `*` facing North. `E` is Behind-Left.
From `*` facing East. `E` is Right/Behind.
I have NEVER faced South or West in this room (except the Westward component of the North-West view of the door? No, facing North covers NW).
I haven't faced South-West.
So `E` is definitely unobserved.
What about `A`, `C`? Facing East from `*`. `A` is front-right? `C` is front-right? Yes. I see "shelf: front-right". That likely corresponds to `A` or `C`.
So `A`, `C`, `D`, `F` are likely observed. `B` is likely observed (empty).
`E` is the main blind spot.
Wait, I need to output the JSON. The prompt asks to select points in unexplored regions.
I'll select `E` as the primary one.
Is `B` unexplored? I faced North. `B` is North-East. 45 degrees right of North. FOV is +/- 45. It's on the edge. I'll include `B` to be safe as I haven't explicitly "seen" the wall there or objects.
The prompt example shows multiple points.
Let's consider `A` and `C`. I see a shelf there. They are "observed".
`D` is observed (near truck).
`F` is observed (path to door).
`B` and `E` are the best candidates.

Actually, looking at the map again.
`*` is at (10,3).
Door `+` is at (6,7).
Facing North from (10,3): FOV is cone from NW to NE.
(6,7) is NW. Observed.
(13,6) is `B`. NE. Likely observed.
(8,0) is `E`. SW. Behind. NOT Observed.
(12,1) is `A`. SE. Front-Right when facing East. Observed (shelf).
(11,1) is `C`. SE. Observed.
(12,3) is `D`. East. Observed (truck?).
(8,4) is `F`. NW. Observed (near door).

So `E` is the strong candidate.
Is there any other?
Maybe `B` if it was occluded?
I'll stick with `E` and maybe `B`.
Let's look at the "fog". The user implies these are candidates for *where to go* or *what is hidden*.
If I haven't seen the laptop, it's likely in `E` or `B`.
I'll list `E` and `B`.

Wait, the prompt says "Select the points that are located in unexplored/unobserved regions."
If I faced North, I saw the empty space towards B?
If I faced East, I see A, C, D.
I haven't faced South. `E` is South-West.
So `E` is definitely unobserved.
Is `B`? Facing North from (10,3). `B` is at (13,6). Vector is (3,3). Angle is exactly +45 deg. That is the limit of FOV (Front-Right). Usually (22.5, 45] is Front-Right. So it is *just* inside or on the edge. I might have missed it or it's unobserved.
I will report `B` and `E`.

One more check.
I entered from the Green Door (6,7). Jumped to Pan.
Where is the Pan?
From door (facing East), Pan was "front-right" (SE).
If door is (6,7), Pan is likely around (10,3) where `*` is.
From `*` facing North (0 deg): I see Green Door (Front-Left). Correct.
From `*` facing East (90 deg): I see Truck (Front), Shelf (Front-Right).
Truck is likely at `D` or near. Shelf is near `A`/`C`.
I have not looked South (180) or West (270).
`E` is at (8,0). From `*` (10,3), `E` is South-West (-135 deg).
`E` has never been in FOV.
`B` is at (13,6). From `*` (10,3), `B` is North-East (+45 deg).
When I faced North, `B` was at the edge.
When I face East, `B` is at Front-Left (+45 deg relative to East? No. Global North-East is Global 45. Facing East is Global 90. Relative is -45. Front-Left).
So `B` should be visible now! "Front-Left".
My observation from Facing East: "truck: front", "shelf: front-right".
I did NOT report anything Front-Left.
So `B` is empty or I missed it.
BUT, if it's empty, it's "observed space" (just empty).
However, `E` is definitely unobserved.
I will output `E`.
What about `F`?
`F` is at (8,4). From `*` (10,3), `F` is West-North-West.
When faced North, `F` is Left (-something).
Green door is at (6,7). `F` is closer.
I likely looked right past `F` to see the door.
It's observed.

I'll go with `E` and `B` to be thorough, but `E` is the strongest.
Wait, let's look at the visual pattern. `B` is in a corner. `E` is in a corner. `A` is in a corner.
`A` has a shelf.
`B` has nothing reported.
`E` has nothing reported.
I'll select `B` and `E`.

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

THINK:
I am currently in Room 3 (the rightmost room based on the map layout). My position is marked by `*`. I am facing East (Right).
I have observed the `truck` (front, near) and `shelf` (front-right, slightly far).
The `pan` (my previous location/jump target) is nearby.
The map shows Room 3 to be ...

###############
#......########
#......########
#......########
#......########
#......########
#......########
######+########
#......########
#......+...B..#
#......#.F....#
#......#.*....#
#......#..D...#
#......#.CA...#
########E.....#
###############

You rotated clockwise 90°. You observe:
• truck: front, near, facing backward
• shelf: front-right, slightly far.
You have a maximum of 13 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• truck: front, near, facing backward
• shelf: front-right, slightly far.
You have a maximum of 13 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am at the 'pan' in Room 3, facing East.
I see the 'truck' (front, near) and 'shelf' (front-right).
I still haven't found the 'laptop'.
I have looked:
- Room 3 from Door (facing East): Saw pan, truck, shelf (South side).
- Room 3 from Pan (facing North): Saw green door.
- Room 3 from Pan (facing East): Saw truck, shelf.
I haven't looked South (behind the pan) or West (back towards the door, but I saw the door from the North facing).
Actually, if I am at the pan and rotate 90 to face East, my FOV is East.
If I rotate another 90 to face South, I cover the corner.
If I rotate another 90 to face West, I look back at the door (which I know is there).
I strongly suspect the laptop is in Room 1 or Room 2, or I missed it in a corner.
Let's review Room 1:
- Start (0,0) facing North: Saw bike, lamp, blue door. (North side)
- At Blue Door facing South: Saw television, cap, green door. (South side)
- This covers North and South. What about East/West walls specifically?
- The bike was front-right (East). The green door is on the "left wall" when facing South (East wall).
- The television was front-right (West? No. Facing South. Front-Right is West. Yes. So TV is West).
- The cap was front-slight-right (West).
- So Room 1: North (door), East (green door, bike), West (TV, cap), Center/South (lamp).
- Seems fairly covered.

Let's review Room 2:
- At Blue Door facing North: Saw vase, rubberduck (Front-Left -> West).
- At Vase facing South: Saw chair (Front-Left -> East?), backpack (Front -> South), blue door (Front-Left -> East? No. From Vase facing South, door is Front-Left. So Door is South-East relative to Vase).
- Vase is likely in the North-West.
- From Blue Door facing North, I saw West (vase, duck). I did *not* see East.
- The 'laptop' might be in the North-East corner of Room 2.
- When I was at the Blue Door facing North, my FOV (90 deg) covered North-West to North-East.
- I saw vase/duck to "front-left" (West).
- I did not report anything "front-right" (East).
- However, if the room is wide, "front-right" might have been empty or I missed it?
- Or maybe "front" was empty?
- Or maybe I should go back to Room 2 and check the East side.

Let's check Room 3 one last time. I haven't faced South.
If the laptop is in the South-East corner (right of shelf?), facing East saw the shelf "front-right". So it's in FOV.
If the laptop is in the South-West corner (behind pan?), facing South would reveal it.
Let's quickly check South in Room 3.
Rotate(90) to face South.
If not there, I jump to green door, go to Room 2.

I am at the 'pan' in Room 3, facing East.
I see the 'truck' (front, near) and 'shelf' (front-right).
I still haven't found the 'laptop'.
I have looked:
- Room 3 from Door (facing East): Saw pan, truck, shelf (South side).
- Room 3 from Pan (facing North): Saw green door.
- Room 3 from Pan (facing Ea...

THINK:
I have found the final object, the 'laptop', in Room 3.
I have now observed all 12 objects and the connecting doors.
- Room 1: blue door, green door, bike, lamp, television, cap.
- Room 2: vase, rubberduck, chair, backpack.
- Room 3: truck, pan, shelf, laptop.

I need to construct the global map based on the observations and movements.
Coordinate System: Start at (0,0) facing North (+y).

Room 1:
- Agent Start: (0,0) facing North.
- Observed:
- lamp: front, mid (say dist 3). Pos: (0, 3).
- bike: front-right, mid. Pos: (2, 2) or (3,3)? Angle ~45. Dist ~3. Let's say (2, 2). Facing left (West).
- blue door: front-right, slightly far (4-8). On front wall. Wait, "front wall" usually means the wall I'm facing (North). So door is on North wall.
- Let's refine based on "JumpTo(blue door), Rotate(180), Observe".
- Jump to blue door -> Pos (X_bd, Y_bd). Facing North.
- Rotate 180 -> Facing South.
- Observed:
- television: front-right (West), slightly far. Facing left (North? No, facing left relative to object? Or relative to me? "facing left" usually means object faces West? No, usually relative to its own frame or global? The prompt says "facing left" in the list. Usually implies global West if North is forward? Or relative to agent? Let's stick to positions first).
- cap: front-slight-right (West), slightly far.
- green door: front-left (East), mid distance, on left wall.
- Constraint: "television is east, near to cap". Wait. I am facing South. East is my Left. West is my Right.
- If TV is front-right, it's West. If Cap is front-slight-right, it's West.
- But prompt says "television is east, near to cap". This contradicts "front-right" if I am facing South.
- Let's re-read: "Assume your current facing direction is called 'north': television is east".
- My current facing is South. So "North" in this local frame is South. "East" in this local frame is West.
- So TV is West. This matches "front-right" (West) when facing South.
- So TV and Cap are West of the blue door.
- Green door is "front-left" (East).
- So Blue Door is North. Green Door is East.
- Coordinates:
- Let Blue Door be (0, 6) approx (slightly far from 0,0).
- From Blue Door (0,6) facing South:
- Green Door: Front-Left. Mid dist (~4). East is +x. South is -y. So (4, 2)? Or (3, 6-3)?
- Green door is on "left wall" (East wall). So x = constant.
- Let's establish room dimensions.
- Blue door on North wall. Green door on East wall.
- Jump to Blue Door. Then Jump to Green Door.
- From Green Door, I entered Room 3.
- Wait, "JumpTo(blue door)" then "Rotate(180)" -> facing North (into Room 2).
- "JumpTo(vase)" -> deep in Room 2.
- "JumpTo(blue door)" -> back to door.
- "JumpTo(green door)" -> move to Green Door.

Let's estimate coordinates more precisely.
Start (0,0) North.
Blue Door: Front-Right, slightly far. Actually initial observe said "front-right".
If I am at (0,0) facing North, and Blue Door is Front-Right, it's at (+x, +y).
Let's guess Blue Door is at (2, 5).
Jump to Blue Door (2, 5).
Rotate 180 -> Face South.
Green Door: Front-Left (East), mid dist. On Left Wall.
If I am at (2, 5) facing South. East is Left.
So Green Door is at (6, 5) or (6, 3)? "Front-left".
Let's assume Room 1 is a rectangle.
Blue door on North wall. Green door on East wall.
Maybe Room 1 is from x=[-2, 6], y=[0, 5]?
Let's fix Blue Door at (0, 5) for simplicity?
Initial view: "blue door: front-right". If at (0,0) facing N, (0,5) is Front. (1,5) is Front-Right.
Let's put Blue Door at (1, 5).
From (1, 5) facing South:
Green Door is Front-Left. Facing South, Left is East. Front is South.
So Green Door is South-East of (1, 5).
Let's say Green Door is at (5, 2).
Distance (1,5) to (5,2) is sqrt(16+9)=5 (Slightly Far, 4-8). Matches.
Green door on "left wall" (East).

Room 2:
Connected via Blue Door (1, 5).
Enter Room 2 (Face North).
Vase: Front-Left (West). Slightly far.
Rubberduck: Front-Slight-Left.
Jump to Vase. Let's say Vase is at (-2, 8).
From Vase (-2, 8) facing South:
Chair: Front-Left (East). Slightly far.
Backpack: Front (South). Near.
Blue Door: Front-Left (East). Slightly far.
If Vase is (-2, 8), Blue Door (1, 5) is Front-Left (South-East). Matches.
Backpack is South of Vase, say (-2, 7).
Chair is South-East, say (0, 7).
Rubberduck was Front-Slight-Left from door. So (-1, 7)?

Room 3:
Connected via Green Door (5, 2).
Enter Room 3 (Face East).
Truck, Pan, Shelf: Front-Right (South-East).
Jump to Pan.
From Pan facing North: Green Door is Front-Left (North-West).
If Green Door is (5, 2), Pan must be South-East. Say (8, -1).
Distance (5,2) to (8,-1) is sqrt(9+9) ~ 4.2 (Slightly far). Matches.
From Pan (8, -1) facing East:
Truck: Front (East). Near. Say (9, -1) or (10, -1).
Shelf: Front-Right (South-East). Slightly far. Say (10, -3).
Rotate 90 (Face South) -> Laptop: Front, Near. Say (8, -2).

Objects Summary:
Agent Final: At Pan (8, -1), facing South (after last rotate).
1. Blue Door: (1, 5).
2. Green Door: (5, 2).
3. Lamp: (0, 3) (Start view front mid).
4. Bike: (3, 3) (Start view front-right mid).
5. TV: (-2, 2) (From Blue Door facing South: Front-Right/West).
6. Cap: (-1, 2) (From Blue Door facing South: Front-Right/West).
7. Vase: (-2, 8).
8. Rubberduck: (-1, 7).
9. Chair: (0, 7).
10. Backpack: (-2, 7).
11. Pan: (8, -1).
12. Truck: (10, -1).
13. Shelf: (10, -3).
14. Laptop: (8, -2).

Refining facings:
- bike: facing left (West).
- television: facing left. From door(S), West is Right. "facing left" in list usually means "Object's left" or relative to view?
- Standard interpretation: "facing left" = West? Or relative to agent?
- "facing left" relative to agent facing South -> East?
- Let's assume absolute directions if possible, or consistent relative.
- "bike: facing left". I was facing North. Left is West. So Bike faces West.
- "television: facing left". I was facing South. Left is East. So TV faces East?
- "cap: facing left". Facing South. Left is East.
- "vase: ...". Facing North.
- "rubberduck: facing left". Facing North. Left is West.
- "chair: facing left". Facing South. Left is East.
- "backpack: facing forward". Facing South. Forward is South.
- "truck: facing backward". Facing East. Backward is West.
- "pan: facing forward". Facing East. Forward is East.
- "laptop: facing left". Facing South. Left is East.

Let's do a sanity check on "Facing".
Usually, "facing left" in observation means the object's front is pointing to the agent's left.
If Agent faces North, Left is West. Object faces West.
If Agent faces South, Left is East. Object faces East.
If Agent faces East, Left is North. Object faces North.
If Agent faces West, Left is South. Object faces South.

Re-evaluating:
- Bike (Agent North): Faces West.
- TV (Agent South): Faces East.
- Cap (Agent South): Faces East.
- Rubberduck (Agent North): Faces West.
- Chair (Agent South): Faces East.
- Backpack (Agent South): Faces South.
- Truck (Agent East): Faces West (Backward).
- Pan (Agent East): Faces East (Forward).
- Laptop (Agent South): Faces East.

Positions cleanup:
Room 1 (Main room):
(0,0) Start.
Lamp (0,3).
Bike (3,3).
Blue Door (1,5).
Green Door (5,2).
TV (-2, 2).
Cap (-1, 2).

Room 2 (North of Blue Door):
Vase (-2, 8).
Duck (-1, 7).
Chair (0, 7).
Backpack (-2, 7).

Room 3 (East of Green Door):
Pan (8, -1).
Truck (10, -1).
Shelf (10, -3).
Laptop (8, -2).

Agent is at Pan (8, -1). Facing South.
Wait, last action: "Rotate(90), Observe()".
Previous state: At Pan, facing East.
Rotate 90 -> Facing South.
So Agent facing South.

Final check on coordinates consistency.
Room 1 is roughly (-2, 2) to (5, 5).
Room 2 is roughly (-2, 7) to (1, 8).
Room 3 is roughly (8, -3) to (10, -1).
Separation seems okay.
Coordinates don't need to be perfect, just topologically consistent and roughly scaled.

One details: "television is east, near to cap".
My coords: TV (-2, 2), Cap (-1, 2).
Cap is East of TV.
Prompt said "television is east, near to cap".
Agent was facing South.
Local "North" is South. Local "East" is West.
So "Television is West of Cap".
My coords: TV x=-2, Cap x=-1. TV is West of Cap. Matches.

Prompt: "truck is north, near to pan".
Agent at Green Door facing East.
Local "North" is East.
Local "East" is South.
So "truck is East of pan".
My coords: Truck (10, -1), Pan (8, -1). Truck is East of Pan. Matches.

Everything seems consistent.

FINAL ANSWER:
```json
{
"agent": {"position": [8, -1], "facing": "south"},
"blue door": {"position": [1, 5], "facing": "south"},
"green door": {"position": [5, 2], "facing": "east"},
"lamp": {"position": [0, 3], "facing": "south"},
"bike": {"position": [3, 3], "facing": "west"},
"television": {"position": [-2, 2], "facing": "east"},
"cap": {"position": [-1, 2], "facing": "east"},
"vase": {"position": [-2, 8], "facing": "south"},
"rubberduck": {"position": [-1, 7], "facing": "west"},
"chair": {"position": [0, 7], "facing": "east"},
"backpack": {"position": [-2, 7], "facing": "south"},
"pan": {"position": [8, -1], "facing": "east"},
"truck": {"position": [10, -1], "facing": "west"},
"shelf": {"position": [10, -3], "facing": "north"},
"laptop": {"position": [8, -2], "facing": "east"}
}
```

THINK:
I have found the final object, the 'laptop', in Room 3.
I have now observed all 12 objects and the connecting doors.
- Room 1: blue door, green door, bike, lamp, television, cap.
- Room 2: vase, rubberduck, chair, backpack.
- Room 3: truck, pan, shelf, laptop.

I need to construct the global ...

{
  "agent": {
    "position": [
      8,
      -1
    ],
    "facing": "south"
  },
  "blue door": {
    "position": [
      1,
      5
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      5,
      2
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      3
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      3,
      3
    ],
    "facing": "west"
  },
  "television": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      -1,
      2
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      -2,
      8
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -1,
      7
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      0,
      7
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -2,
      7
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      -1
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      10,
      -3
    ],
    "facing": "north"
  },
  "laptop": {
    "position": [
      8,
      -2
    ],
    "facing": "east"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "south"
  }
}

THINK:
I have successfully found the last missing object, the 'laptop', by rotating to face South in Room 3.
I am currently located at the position of the 'pan'.
I am facing South.
I need to produce a Local Cognitive Map relative to my current position and orientation.
The only object in my current FOV (from the last observation) is the 'laptop'.
The observation was: `laptop: front, near, facing left`.
Frame of reference:
- Origin: Agent (at 'pan').
- +y: Agent's facing direction (South).
- +x: Right (West).
- -x: Left (East).
- -y: Backward (North).

Observation details:
- `laptop`: "front, near".
- "Front" means generally along the +y axis.
- "Near" corresponds to a distance bin (0, 2]. I'll estimate coordinates. Let's say [0, 2] or [0, 1]. Since it's "near", [0, 1] or [0, 2] is appropriate.
- "facing left". In the local frame (+y is forward), "left" is the -x direction. So the laptop is facing -x.

Wait, let's double check the coordinate system.
If +y is forward:
Left is -x.
Right is +x.
The prompt says: "when facing +y: +x -> right, -x -> left".
So "facing left" means the object's orientation is along the -x axis.

Coordinates for the laptop:
It is "front". So x should be close to 0, y should be positive.
It is "near" (dist <= 2). So maybe y=1 or y=2.
Let's assign it `[0, 2]` for simplicity (mid-point of "near" range usually implies 1 or 2, 2 is safer for grid separation, or 1 for very close). "Near" is (0,2]. Let's use `[0, 1]`.
Actually, previously for "near", I might have seen objects at 1 or 2. Let's pick `[0, 1]` or `[0, 2]`. I'll go with `[0, 1]` as it is very close.
Facing: "-x".

Are there any other objects?
The observation only listed the laptop.
Wait, "pan" is where I am standing. It is not in the FOV (I am on it).
Previous observation (Rotate 90 to East) saw 'truck' and 'shelf'.
Current observation (Rotate 90 to South) saw ONLY 'laptop'.
So the JSON should only contain the laptop.

Wait, I should confirm the facing.
"laptop ... facing left".
If I am facing South (+y local), "left" is East (-x local).
So the laptop is facing East.
In local coordinates: `facing: "-x"`.

Let's refine the position. "near" usually maps to 1-2 units. I will use `[0, 1]`.

One detail: The prompt asks for "Local Cognitive Map".
"Include all objects and doors in your current field of view".
My current FOV only contains the laptop.

So the JSON is:
```json
{
"origin": "agent",
"objects": {
"laptop": {"position": [0, 1], "facing": "-x"}
}
}
```

Wait, is there anything else?
The prompt says "Observe action ... reports objects ... from your current position in your FOV."
The last output was "You observe: • laptop: front, near, facing left."
Nothing else.
So the map is correct.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"laptop": {"position": [0, 1], "facing": "-x"}
}
}
```

THINK:
I have successfully found the last missing object, the 'laptop', by rotating to face South in Room 3.
I am currently located at the position of the 'pan'.
I am facing South.
I need to produce a Local Cognitive Map relative to my current position and orientation.
The only object in my current ...

{
  "origin": "agent",
  "objects": {
    "laptop": {
      "position": [
        0,
        1
      ],
      "facing": "-x"
    }
  }
}

{
  "laptop": {
    "position": [
      0,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "laptop": {
      "position": [
        0,
        1
      ],
      "facing": "-x"
    }
  }
}

{
  "laptop": {
    "position": [
      0,
      2
    ],
    "facing": "east"
  }
}

THINK:
I have successfully found the missing object, the 'laptop', by rotating to face South in Room 3.
Now I need to address the Fog Probe task.
The map provided shows a grid layout.
Room 1 is likely the top-left section (connecting via a door on its South wall to Room 2? No, let's trace coordinates).
My starting position (0,0) in the prompt corresponds to the agent's initial location.
Wait, the map legend says (0,0) is bottom-left. The prompt said "initial position is in room 1... treat your initial position as origin (0,0)".
This might be a coordinate transformation issue.
Let's look at the map structure visually.
There are three rooms.
Room 1 (Top Left, 6x7 approx): Has a door '+' on its South wall connecting to Room 2.
Room 2 (Bottom Left, 6x7 approx): Connects to Room 1 (North) and Room 3 (East).
Wait, the prompt said "Rooms connect via doors on vertical (front/back) or horizontal (left/right) walls."
The map shows:
Top-Left Room: 6x7. Door on bottom wall.
Bottom-Left Room: 6x7. Door on top wall (connects to Top-Left). Door on right wall (connects to Bottom-Right).
Bottom-Right Room: 6x7. Door on left wall.
This matches the connectivity: Room 1 (Top) -> Blue Door -> Room 2 (Bottom Left) -> Green Door -> Room 3 (Bottom Right).
Wait, the prompt said "initial position is in Room 1".
I found the Blue Door on the "front" (North) wall of Room 1?
Wait, step 1 observation: "blue door: front-right, ... on front wall". I was facing North. So Blue Door is North of me.
So Room 1 is the *bottom* room?
Let's re-read Step 1: "You observe... blue door: front-right... on front wall." (facing North).
If Blue Door is on the North wall of Room 1, then Room 2 is North of Room 1.
Map:
Bottom-Left Room (Room 1). Door on Top Wall.
Top-Left Room (Room 2).
But the Map shows a door between Top-Left and Bottom-Left.
If I started in Bottom-Left facing North, I see the door on the North wall. This matches.
So Room 1 is Bottom-Left.
Then I went to Blue Door (North), turned South (saw Room 1).
Then turned North (saw Room 2). Room 2 is Top-Left.
Then I saw Green Door. Wait, where was the Green Door?
Step 2 (at Blue Door facing South, looking into Room 1): "green door: front-left... on left wall".
If I am at the North wall of Room 1 facing South, "Left" is East.
So the Green Door is on the East wall of Room 1.
So Room 1 connects to Room 3 on the East.
Let's check the map again.
Map shows:
Bottom-Left Room. Door on Top (to Top-Left). Door on Right (to Bottom-Right).
Yes, Bottom-Left Room (Room 1) has a door on Top (Blue) and Right (Green).
Wait, Step 4: "Jumped to green door... rotated -90... observe... pan... truck".
Step 4 context: "Jump to green door" from Blue door. Blue door is on North wall. Green door is on East wall.
I went to Green Door.
The map shows a door on the right wall of the Bottom-Left room. This leads to the Bottom-Right room.
So Room 3 is Bottom-Right.
Current Position: I am in Room 3 (Bottom-Right).
I am at the 'laptop'.
Previous action: "Rotated 90 deg" (Step 6) to face South.
So I am facing South.
My position '*' is shown in the Bottom-Right room.
The points A and B are in the Bottom-Right room.
A is North of me. B is South-West of me (or West?).
Let's look at the map string specifically.
Points:
A is at roughly column 9, row 5 (counting from bottom 0).
* is at roughly column 10, row 5.
B is at roughly column 9, row 4.
The room boundaries for Room 3 (Bottom-Right) seem to be approx x=8 to x=14, y=1 to y=7.
I am at '*' (laptop). I just found the laptop facing South.
I have observed:
- From Green Door (East facing): Saw Truck, Pan, Shelf. (Central/East part)
- From Pan (North facing): Saw Green Door (West).
- From Pan (East facing): Saw Truck, Shelf.
- From Pan (South facing): Saw Laptop.
So I have looked North, East, South from the Pan/Laptop area.
The 'Pan' and 'Laptop' are close.
The point '*' is my current position.
I have observed the area around me.
A is North-West of me (next to wall).
B is South-West of me (next to wall).
Have I seen these areas?
From Green Door (facing East), I looked into the room. A and B are "near" the door (West side of Room 3).
From the Green Door, A and B would be in the "front" or "front-left/right" area?
Green Door is at x=7 (approx), y=4 (approx). Facing East.
Room 3 spans x=8..14.
A is at x=9, y=5.
B is at x=9, y=4.
When standing at Green Door (x=7, y=4) facing East:
- (9,4) [B] is Front (Distance 2). Visible.
- (9,5) [A] is Front-Left (Angle approx 26 deg). Visible.
So A and B should have been covered by the observation at the Green Door.
However, "fog" implies "unexplored/unobserved".
Did I definitely see them?
Step 4 Observation (at Green Door): "truck: front-right... pan: front-right... shelf: front-right".
All reported objects were Front-Right (South-East).
Why?
Maybe A and B are empty space? The observation only lists objects.
But "unexplored" usually means "grid cells not covered by FOV".
My FOV at Green Door (facing East) covers [-45, 45] relative to East. i.e., North-East to South-East.
B (9,4) is straight East (0 deg). Visible.
A (9,5) is East-North-East. Visible.
Wait, if I observed "truck, pan, shelf" which are all Front-Right (South-East), did I see North-East?
The FOV is 90 degrees. If I face East, I see NE to SE.
The report listed objects. If A and B contain no objects, they wouldn't be listed.
But are they "observed"? Yes, the cells were within FOV.
Is there any reason to think they are unobserved?
Maybe occlusion?
No objects were reported "front" or "front-left".
Does that mean there's a wall blocking? No, it's an open room.
Maybe the prompt implies "points located in unexplored/unobserved regions" based on *current* status?
No, "unexplored" means never seen.
Let's check the previous steps again.
Room 1 (Bottom Left): Fully explored.
Room 2 (Top Left): Visited 'vase'. Faced South. Saw 'chair, backpack'. Faced North (from door). Saw 'vase, duck'.
Did I see the North-East corner of Room 2?
From Blue Door (facing North), I saw West (Front-Left). Did I see East?
My FOV (facing North) is NW to NE.
If nothing reported in NE, and space is empty, it's observed.
Room 3 (Bottom Right):
From Green Door (East): Saw SE (Truck, Pan, Shelf).
Did I see NE? (Where A is?)
If A is at (9,5) and Door is (7,4). Angle is atan(1/2) = 26 deg. Within FOV.
Did I see B? (9,4). Angle 0. Within FOV.
So A and B are in the observed region.
Is there any trick?
"Use binned labels... Front-Right...".
If I only reported objects in Front-Right, does that mean I didn't see Front-Left?
No, I report what is there. If nothing is there, I report nothing. But the space is "observed".
However, the Fog Probe usually asks for points that are *candidates* for something or just strictly "unobserved".
"Select the points that are located in unexplored/unobserved regions."
If I stood at (7,4) and looked East, I saw (9,4) and (9,5).
So A and B are observed.
Are there any other points?
The map shows points A and B. That's it.
If both are observed, the answer is empty.
But usually, these questions imply some points are unobserved.
Let's re-read the "fog" definition.
Usually, it means "cells never within the FOV cone of any Observe action".
Let's trace the FOV cones carefully.
1. Start (Room 1, say 3,3). Face North. Observe. Saw Blue Door (North Wall).
- Cone: NW to NE.
2. Jump to Blue Door (Room 1 North Wall, say 3,6). Face South. Observe.
- Cone: SE to SW. (Room 1 covered).
3. Face North (into Room 2). Observe.
- Cone: NW to NE.
- Saw Vase (Front-Left).
4. Jump to Vase (Room 2, say 1,8). Face South. Observe.
- Cone: SE to SW.
- Saw Chair, Backpack.
5. Jump to Green Door (Room 1 East Wall, say 6,3). Face East (into Room 3). Observe.
- Cone: NE to SE.
- Saw Truck, Pan, Shelf (Front-Right i.e. SE).
- A is at (9,5). Relative to (6,3), dx=3, dy=2. Angle ~33 deg. (Front-Right).
- B is at (9,4). Relative to (6,3), dx=3, dy=1. Angle ~18 deg. (Front-Right).
- Wait, if they are Front-Right, they are in the cone.
- Why did I think A was "Left"?
- Green Door is on the "left wall" of Room 1 (facing South). So it's East wall.
- Y axis is North.
- Door at (6,3).
- A at (9,5).
- Facing East (0 deg).
- Vector to A: (3, 2). Angle +33 deg.
- Bins: 0-22.5 is Front-Slight-Right. 22.5-45 is Front-Right.
- So A is Front-Right.
- Vector to B: (3, 1). Angle +18 deg.
- Bin: Front-Slight-Right.
- Step 4 reported: Truck, Pan, Shelf.
- Did it report empty space? No.
- But the cells A and B are geometrically within the cone.
- So they are OBSERVED.
- Is there any ambiguity?
- Maybe the Green Door is at (6,4) and A is (9,5)? Angle 18 deg.
- Regardless, facing East captures NE and SE. A and B are East of the door.
- Unless there's an obstacle? "Door block vision...".
- I am at the door.
- So A and B are observed.

Is there any point I missed?
Maybe Room 2 North-East corner?
Map doesn't show points there. Only A and B in Room 3.
Wait, look at the ASCII map provided in the prompt.
The '*' is at (10,5).
A is at (9,5).
B is at (9,4).
My last action: At '*' (Laptop), facing South.
Observe(): FOV South (SE to SW).
A (9,5) is West of me (at 10,5).
B (9,4) is South-West of me.
From '*' facing South:
- B (9,4) is dx=-1, dy=-1. Angle -135 (Back-Left). NOT in FOV.
- A (9,5) is dx=-1, dy=0. Angle -90 (Right). NOT in FOV.
So A and B were NOT observed in the LAST step.
But were they observed in previous steps?
Step 4 (Green Door, facing East):
- Door at x=7.
- A (9,5): dx=2, dy... (depending on door Y).
- If Door Y=5 (centered?): A is straight East.
- If Door Y=4: A is NE.
- Either way, facing East sees A and B.
- So A and B *were* observed in Step 4.

Is the question "currently visible"?
"Select the points that are located in unexplored/unobserved regions."
Standard definition: Unexplored = never seen.
So A and B are explored.
Is there a catch?
Maybe the map legend? A and B are "Candidates".
Maybe I need to query them? No.
Maybe I'm wrong about the Green Door observation.
Step 4: "truck: front-right... pan: front-right... shelf: front-right".
Implies objects are in SE.
Nothing reported in NE.
Does "Nothing reported" = "Empty space seen" or "Not seen"?
In these tasks, usually "Nothing reported" = "Saw nothing".
So the region was observed and found empty.
Thus A and B are observed.

Let's check the "fog" output format.
"unexplored": ["A", "C"]
If all are explored, output empty list?
Or maybe I miscalculated the Green Door position.
Green Door is on the "Left Wall" of Room 1 (facing South).
Room 1 is Bottom-Left.
Left Wall of Room 1 is the West Wall?
Wait.
Facing South. Left is East.
Right is West.
So Green Door is on East Wall of Room 1. Correct.
So I enter Room 3 from the West. I face East.
Correct.

What if Room 3 is L-shaped?
Map:
########
#......#
#A*....#
#B.....#
#......#
########
It looks rectangular.
The door '+' is at the West wall of this room.
Looking East covers the room.
So A and B should be observed.

Wait, look at the ASCII map again.
The door '+' is at column 7, row 6?
No, count from bottom.
Row 0: ###############
...
Row 6: #......#A*....#
Row 5: #......#B.....#
Row 4: #......#......#
Row 3: ########......#
Row 2: ############### (No, bottom is row 0)
Let's count rows up from bottom-left corner '#'.
Row 0: ###############
Row 1: ########......# (Room 3 starts)
Row 2: #......#......#
Row 3: #......#B.....# (B is here)
Row 4: #......#A*....# (A and * are here)
Row 5: #......#......#
Row 6: #......+......# (This looks like a door?)
Row 7: #......########
Wait, the symbol '+' appears in two places.
1. Row 9, Col 6. (Between Room 1 and 2?)
2. Row 6, Col 6? No.
Let's find '+'.
Row 7 (from bottom): "######+########" -> Door at Col 6. (Connecting Top and Bottom rooms).
Row 5 (from bottom): "#......+......#" -> Door at Col 7? No, it's "#......#......#".
Wait, let's copy the map to a text editor grid.
Line 1: ###############
Line 2: #......########
Line 3: #......########
Line 4: #......########
Line 5: #......########
Line 6: #......########
Line 7: #......########
Line 8: ######+######## (Door 1)
Line 9: #......########
Line 10: #......+......# (Door 2?) No.
Wait, let's look at the "Map:" block in the prompt.
15 rows?
Rows:
15: ###############
14: #......######## (Room 2 Top)
13: #......########
12: #......########
11: #......########
10: #......########
09: #......########
08: ######+######## (Door between Room 2 and Room 1)
07: #......######## (Room 1 Top)
06: #......+......# (Door between Room 1 and Room 3?)
Wait, "+" at (7, 6) approx?
05: #......#......# (Wall between Room 1 and Room 3?)
04: #......#A*....#
03: #......#B.....#
02: #......#......#
01: ########......#
00: ###############

Wait, look at Row 06: `#......+......#`.
This `+` is at x=7? No.
`#` (0) `.`(1)...... `+` is at 7?
The wall is at 7. `#......#`
If there is a `+` in the vertical wall, it connects Left and Right.
Let's look at Row 6: `#......+......#`.
Wait, is it a `+` or a `#`?
Prompt Map:
`#......+......#`
It has a `+` at column 7.
So there is a door connecting Room 1 (Left) and Room 3 (Right) at Row 6.
Room 3 spans Rows 1-6?
The `+` is at Row 6.
My position `*` is at Row 4.
A is at Row 4.
B is at Row 3.
(Using 0-indexed from bottom).
If the door is at Row 6 (North end of the wall separating rooms), and I stand there facing East...
I see Rows 1-11 in the East direction?
No, Room 3 is bounded by walls.
Room 3 seems to be Rows 1-6, Cols 8-14.
If Door is at Row 6 (Top-Left corner of Room 3):
Standing at Door (7,6) facing East.
My FOV covers East.
Points A (9,4) and B (9,3) are South-East of the door.
Angle from (7,6) to (9,4): dx=2, dy=-2. Angle -45 deg. (Front-Right).
Angle from (7,6) to (9,3): dx=2, dy=-3. Angle -56 deg. (Right).
Constraint: FOV is 90 degrees ([-45, 45]).
So anything with angle > 45 or < -45 is NOT visible.
Angle to A (9,4): -45 deg. This is on the boundary. Usually inclusive? Or exclusive?
"Bins... (22.5, 45] -> front-right". So 45 is visible.
Angle to B (9,3): tan(3/2) = 56 deg. > 45. NOT VISIBLE.
So B is definitely UNEXPLORED from the door.
What about from other positions?
I jumped to 'pan'. Where is 'pan'?
Step 4 observation: "pan: front-right, mid distance" (from door).
Door (7,6). Pan is SE.
Then I jumped to Pan.
Rotated -90 (to face North).
Saw Green Door (Front-Left).
Rotated 90 (to face East).
Saw Truck, Shelf.
Rotated 90 (to face South).
Saw Laptop (at `*`).
My position `*` is (10,4).
From `*` (10,4) facing South:
FOV is South (SE to SW).
B is at (9,3).
Vector from (10,4) to (9,3): dx=-1, dy=-1. Angle -135 (South-West?).
Wait, facing South (0 relative).
South is -90 global? Or 180 global?
"Facing South" -> North is behind.
Vector (-1, -1) is South-West global.
Relative to South facing:
Front is South.
Right is West.
Left is East.
B (-1, -1) is West-South.
Angle relative to South: 45 degrees to the Right.
So "Front-Right".
Is it within 45 degrees? Yes.
So B should be visible from `*` facing South.
Wait, let's check coordinate geometry again.
Source (10,4). Target (9,3).
Facing South (Direction (0, -1)).
Vector D = (-1, -1).
Dot product: 0*(-1) + (-1)*(-1) = 1.
Length D = sqrt(2). Length Facing = 1.
Cos theta = 1 / sqrt(2).
Theta = 45 degrees.
So B is exactly on the edge of the FOV (45 deg).
If edge is inclusive, B is observed.

What about A?
A is at (9,4).
From `*` (10,4) facing South.
Vector (-1, 0). (West).
Relative to South: 90 degrees Right.
Not in FOV (max 45).
So A is NOT observed from `*` facing South.
Was A observed before?
From Door (7,6) facing East.
A (9,4). Vector (2, -2).
Facing East (1, 0).
Dot product: 2.
Length D = sqrt(8).
Cos theta = 2 / sqrt(8) = 1/sqrt(2).
Theta = 45 degrees.
So A is on the edge (Front-Right).
If inclusive, A is observed.

From Pan?
Where is Pan?
Observed from Door (7,6) as "Front-Right, mid distance" (distance 2-4).
A (9,4) is distance 2.8 from door.
Maybe Pan IS A? Or near A?
"pan: front-right".
If I jumped to Pan.
Let's say Pan is at (9,4).
Then I am at A.
Then I rotated...
But currently I am at `*` (Laptop).
Map shows `*` at (10,4) and A at (9,4).
So A is a neighbor.
If I am at (10,4) and A is (9,4).
From Door (7,6), I saw Pan.
From Pan, I saw...
Did I ever look WEST from inside the room?
1. Door (Face East) -> Saw A (edge).
2. Pan (Face North) -> Saw Door (NW).
- Pan position? If Pan is (9,4). Face North (0,1).
- A (9,4) is self? Or if Pan is (10,4).
- If Pan is (10,4). Face North. A (9,4) is West (-1,0). Left (90 deg). Not in FOV.
3. Pan (Face East) -> Saw East. A is West. Not in FOV.
4. Laptop (Face South) -> A is West. Not in FOV.

So A (9,4) was seen from the Door ONLY if 45 degrees is inclusive.
B (9,3) was seen from the Door?
Vector (2, -3). Angle > 45. Not seen from Door.
Was B seen from Laptop (10,4) facing South?
Vector (-1, -1). Angle 45. Edge.
If 45 is inclusive, B is seen.
If 45 is exclusive, B is NOT seen.
"FOV is 90 degrees". Usually means +/- 45.
Standard implementation often uses strict inequality or inclusive.
"Bins... (22.5, 45] -> front-right".
The bracket `]` implies inclusive.
So 45 degrees is visible.
So A is visible from Door.
B is visible from Laptop.

Are there other constraints?
"Rooms connect via doors...".
The map shows the door at (7,6).
Room 3 bottom-left is (8,1).
So Room 3 height is large.
Is it possible the door is lower?
Step 4: "green door: front-left, mid distance, on left wall" (from Pan facing North).
If Pan is at (10,4).
North is (0,1).
Green Door at (7,6).
Vector (-3, 2).
Angle relative to North: atan(-3/2) = -56 degrees.
This is OUTSIDE FOV (Left is >45?).
Wait. FOV is +/- 45.
-56 is "Left". Not "Front-Left".
"Front-Left" is [-45, 0].
"Left" is [-135, -45]? No, usually "Left" is a cardinal direction or a rotation.
But "Observe" reports "Front-Left".
Bin: "[-45, -22.5) -> front-left".
If the door was reported as "front-left", it must be within -45.
So angle must be > -45.
My geometric deduction of Pan=(10,4) and Door=(7,6) gives angle -56.
Contradiction.
So either:
1. Pan is further North? e.g. (9,5).
- Vector to (7,6): (-2, 1). Angle atan(-2) = -63. Worse.
2. Pan is further South? e.g. (10,2).
- Vector to (7,6): (-3, 4). Angle atan(-3/4) = -37. OK!
- So Pan is South-ish. (10,2).
- If Pan is (10,2).
3. Door is further South? e.g. (7,4).
- If Door is (7,4).
- From Pan (10,4) facing North. Vector (-3, 0). Angle -90 (Left). Not Front-Left.
- From Pan (10,2) facing North. Vector (-3, 2). Angle -56.

Let's reconsider the "Green Door on Left Wall" observation.
Step 2: At Blue Door (North wall), facing South. Green Door is "Front-Left".
Blue Door (say 3, 10). Facing South.
Green Door is East-South.
Vector (dx, dy). dx>0, dy<0.
Relative to South: Front-Left means East.
So Green Door is East of Blue Door and South of Blue Door.
This is consistent with Green Door being on the East wall of Room 1.
If Room 1 is (0..6, 0..7). Green Door is at (6, y).
Step 4: At Green Door (6, y), facing East.
Saw Pan "Front-Right" (SE).
So Pan is South of the door.
Jump to Pan. Rotate -90 (Face North).
Saw Green Door "Front-Left".
Vector from Pan to Door must be Front-Left (Angle 0 to -45 relative to North).
So Door is North-West of Pan.
And angle is small (<45).
So dy (North) > dx (West).
Door is (6, y). Pan is (x_p, y_p).
x_p > 6. y_p < y.
Vector (6-x_p, y-y_p).
(y-y_p) > |6-x_p|.
Example: Pan at (7, 3). Door at (6, 5).
Vector (-1, 2). Angle atan(-0.5) = -26 deg. Fits "Front-Left".
So Pan is South-East of Door, and Door is North-West of Pan.

Now, Map Analysis with this alignment.
Door is at (7, 6) in the map?
Row 6 has `+`.
If Door is (7, 6).
Pan must be South-East. e.g. (8, 4).
My current position `*` is at Laptop.
Observation at Step 6 (from Pan, facing East): "Truck (front), Shelf (front-right)".
Observation at Step 8 (from Pan, facing South): "Laptop (front)".
So Laptop is South of Pan.
If Pan is (8, 4), Laptop is (8, 3)?
Or (8, 2)?
Map shows `*` at Row 4.
So Laptop is at Row 4.
Then Pan must be at Row 5 or 6?
If Pan is North of Laptop, and Laptop is at Row 4. Pan >= 5.
But Pan is South of Door (Row 6).
So Pan could be Row 5.
If Pan is (8, 5).
Door (7, 6). Vector (-1, 1). Angle -45. Borderline.
Laptop `*` (8, 4).
From Pan (8, 5) facing South. Laptop (8, 4) is Front (0 deg). Matches.
So consistent: Door (7, 6). Pan (8, 5). Laptop (8, 4).
Wait, map shows `*` at (10, 4).
Let's assume the map ASCII is spatially accurate relative to itself.
`*` is at x=10, y=4.
So Laptop is (10, 4).
Then Pan is North of Laptop -> (10, 5).
Door is (7, 6).
From Pan (10, 5) facing North.
Vector to Door (7, 6) is (-3, 1).
Angle atan(-3/1) = -71 deg.
This is NOT "Front-Left" (max -45).
This contradicts "Green Door: front-left".
Unless "Front-Left" bin is wider?
"[-45, -22.5) -> front-left".
Beyond -45 is "Beyond FOV" (or Left/Right in some models, but instructions say "otherwise -> beyond-fov").
So Pan CANNOT be at (10, 5) if Door is at (7, 6).

Maybe Door is not at (7, 6)?
Row 6: `#......+......#`.
Maybe the `+` is irrelevant?
Or maybe Room 1 is Top-Left?
If Room 1 is Top-Left. Blue Door on South Wall.
Face South (into Room 2).
Jump to Blue Door. Face North (back to Room 1).
Face South (Room 2).
Green Door on Left (East) Wall.
Room 3 is Top-Right.
If Room 3 is Top-Right (Rows 8-14).
My `*` is at Row 4.
This contradicts.

Let's trust the Map's `*` position and A/B relative to it.
`*` is at (10, 4).
A is at (9, 4).
B is at (9, 3).
(Assuming 1-step increments).
A is West of `*`.
B is South-West of `*`.

Check visibility of A (9,4) and B (9,3).
1. From Door.
Where is the door?
If Pan (where I saw the door from) is near `*` (since I jumped to Pan, then rotated, then rotated... and `*` is Laptop found near Pan).
Actually, I was at Pan. Saw Laptop "Front, Near".
So Laptop is near Pan.
If Laptop is (10,4), Pan is likely (10,5).
We established this contradicts Door at (7,6).
So Door must be elsewhere.
Maybe Door is at (7, 4)?
If Door is (7, 4).
From Pan (10, 5) facing North. Vector (-3, -1). Behind.
From Pan (10, 5) facing West? No, I faced North.
Maybe Pan is at (10, 3)?
From Pan (10, 3) facing North.
Door (7, 4). Vector (-3, 1). Angle -71. No.
Maybe Door is at (7, 8)?
From Pan (10, 5) facing North.
Door (7, 8). Vector (-3, 3). Angle -45. Fits!
So Door could be at (7, 8).
If Door is at (7, 8).
From Door (7, 8) facing East.
A (9, 4). Vector (2, -4). Angle -63. Not visible (max 45).
B (9, 3). Vector (2, -5). Angle -68. Not visible.
So A and B were NOT seen from Door.

2. From Pan (10, 5).
facing North: Saw Door. (FOV NW..NE).
A (9, 4) is SW. Not seen.
B (9, 3) is SW. Not seen.
facing East: Saw Truck. (FOV NE..SE).
A (9, 4) is SW. Not seen.
B (9, 3) is SW. Not seen.
facing South: Saw Laptop (10, 4). (FOV SE..SW).
A (9, 4). Vector (-1, -1) from Pan? No, A is West of Laptop.
If Pan is (10, 5). A is (9, 4).
Vector (-1, -1). Angle -135 from North?
Relative to South (facing):
Front is South.
Right is West.
Vector (-1, -1) is South-West.
Angle 45 deg Right.
So A (9, 4) is on the edge (45 deg). Visible?
B (9, 3). Vector (-1, -2). Angle atan(0.5) = 26 deg Right. Visible!
So B is visible from Pan facing South.
Wait, I faced South from Pan.
"You rotated clockwise 90°. You observe: laptop: front, near...".
Action was "Rotate(90)".
Previous facing was East.
East + 90 = South.
So I faced South at Pan.
I saw Laptop.
Did I see B?
B is at (9, 3). Pan at (10, 5).
Vector (-1, -2). Relative to South: Front-Right.
Angle 26 deg.
Mid distance (sqrt 5 = 2.2).
Should have been observed.
Was it reported?
"laptop: front, near".
Only laptop reported.
Does that mean B is empty?
If B is empty, it is "observed".
"Select the points that are located in unexplored/unobserved regions."
If B was observed (empty), it is not unexplored.

What about A (9, 4)?
From Pan (10, 5) facing South.
Vector (-1, -1). Angle 45 deg.
If 45 is inclusive, A is observed.
If exclusive, A is unobserved.
And A (9, 4) is also West of `*` (10, 4).
From `*` (Laptop) facing South.
Wait, I am currently AT `*`?
"You rotated... You observe... laptop...".
Usually "You observe X" means X is near you.
"JumpTo(laptop)" was not performed.
I am at Pan.
I see Laptop.
So `*` on map denotes Agent Position.
So `*` is Pan.
Map legend: `*`: Agent's current Position.
I am at Pan.
So Pan is (10, 4) on the map.
A is (9, 5).
B is (9, 4).
(Based on ASCII relative positions).
`*` is at (10, 4).
A is (10, 5)? No.
`#......#A*....#`
A is left of `*`.
So A is (9, 4). `*` is (10, 4).
`#......#B.....#` (Row below)
B is at (9, 3).
So:
Pan (`*`) = (10, 4).
A = (9, 4).
B = (9, 3).

Re-evaluate Visibility from Pan (`*`, 10, 4).
1. Facing North:
- A (9, 4) is West (-1, 0). Left (90 deg). Not in FOV.
- B (9, 3) is SW. Not in FOV.
2. Facing East:
- A is West.
- B is SW.
3. Facing South (Current):
- A (9, 4). Vector (-1, 0). Right (90 deg). Not in FOV.
- B (9, 3). Vector (-1, -1). SW. Front-Right (45 deg).
- If 45 inclusive: Observed.
- If 45 exclusive: Unobserved.

What about from Door?
If Pan is (10, 4).
Door must be such that Pan is SE and Door is NW of Pan (for "Front-Left" view from Pan).
Door at (7, 7)?
Vector Pan->Door: (-3, 3). Angle 45. (Front-Left edge).
Vector Door->Pan: (3, -3). Angle -45. (Front-Right edge).
If Door is (7, 7).
From Door facing East:
A (9, 4). Vector (2, -3). Angle -56. Not in FOV.
B (9, 3). Vector (2, -4). Angle -63. Not in FOV.
So A and B not seen from Door.

So A is definitely unobserved (90 deg from Pan facing South).
B is edge case from Pan facing South. (45 deg).
Given "unexplored", and B is a candidate point.
Usually points are centered in cells.
B (9, 3) relative to Pan (10, 4).
Angle is exactly 45.
In many grid worlds, diagonals are visible.
But A (9, 4) is definitely not visible from Pan facing South (90 deg).
Was A seen from Pan facing North?
Vector (-1, 0). 90 deg Left. No.
From Pan facing East? Behind.
So A is Unexplored.

What about B?
If B is unobserved, answer is A, B.
If B is observed, answer is A.
Common pattern: Walls block?
No walls between Pan and B.
Let's assume standard FOV < 45 strictly?
Or typically "candidates" are the unobserved ones.
If B is unobserved, why?
Angle 45.
Maybe FOV is narrower?
Or maybe A and B are the answer.

Let's check if A or B were seen from Room 1 or 2?
No, walls.

Let's check if I ever faced West in Room 3?
No.
East, then North, then East, then South.
Never West.
A is West of Pan.
B is South-West of Pan.
Facing South covers SW?
Yes, if |angle| <= 45.
SW is exactly 45.
If strictly less, then B is unobserved.
If inclusive, B is observed.
A is West (90 deg). Unobserved.

Which is more likely?
In these problems, "candidates" usually highlight the unknown.
Both A and B are in the "West" side of the room which I never directly faced.
I faced North (seen NW door).
I faced East (seen NE, SE).
I faced South (seen SE, SW?).
But A is strictly West.
So A is definitely unobserved.
B is on the diagonal.
If I have to choose, A is certain. B is likely unobserved if conservative.
However, I will output both if the map suggests a cluster of unobserved points.
Wait, Map shows A and B.
If B was observed, why label it?
Usually all labeled points are valid candidates for the condition unless proven otherwise.
If B was on the edge, it's safer to classify as unobserved (foggy).
Also, from Door (7, 7), A and B are "down and right" but angle > 45.
So definitely not seen from Door.
So only chance was Pan facing South.
If FOV is standard 90 deg (45 half-angle).
The "Front-Right" bin is (22.5, 45].
So 45 is included in the bin.
So B *should* be observed.
But observe report: "laptop: front, near".
B is "mid distance" (sqrt 2 = 1.41? No, 1 step is 1.0? Dist bins: 0-2 near, 2-4 mid).
Distance sqrt(2) * scale?
If coords are integers. Dist 1.41.
Bin: (0, 2] -> near.
So B would be "near".
Laptop is "near".
If B is not reported, and it's in FOV, then B is empty space.
So B is observed empty space.
So B is explored.

So A is the only unobserved one?
A (9, 4) from Pan (10, 4).
Distance 1.
Angle 90 deg (Right).
Bin: "Otherwise -> beyond-fov".
(22.5, 45] is Front-Right.
(45, ...?
Constraint: "Egocentric angle bins... (22.5, 45] -> front-right, otherwise -> beyond-fov."
Wait.
If angle is > 45, it is beyond FOV.
So B (45 deg) is Front-Right (Included).
A (90 deg) is Beyond FOV.
So A is Unobserved.
B is Observed.

Final check on B.
Angle is 45.
Bin (22.5, 45].
45 is in bin.
So B is observed.

Wait, is B at (9, 3) and Pan at (10, 4)?
Vector (-1, -1).
Angle is 45.
So B is observed.
A is (9, 4). Vector (-1, 0). Angle 90. Not observed.

Is there any chance Pan is at (11, 4)?
Then A (9, 4) is (-2, 0). Not seen.
B (9, 3) is (-2, -1). Angle atan(0.5) = 26 deg. Seen.
So B is seen regardless.
A is not seen regardless.

So answer should be ["A"].

What if A is not (9, 4)?
Map:
`#......#A*....#`
A is immediately left of `*`.
Yes.
So A is definitely unobserved.

Is there any other point?
The prompt asks to "Select the points".
Only A and B are labeled.
So choice is A, B, or both.
My logic: A is unobserved. B is observed.
So ["A"].

Let's double check B visibility.
"FOV is 90°".
Usually means a cone.
On a grid, (x-1, y-1) is visible from (x, y) facing South?
South is (0, -1).
Vector (-1, -1).
Angle 45.
Yes, usually visible.
If B is observed, why is it labeled?
Maybe to trick?
Or maybe my coordinate system is slightly off?
If `*` is (10.5, 4.5)? (Continuous coordinates).
"Every object including you is a point at integer (x, y) coordinates."
So integer.
So logic holds.

Final Decision: A is unobserved. B is observed.
Output: ["A"].

Wait, I should check if A was seen from anywhere else.
From Door (7, 8) facing East?
A (9, 4). Vector (2, -4). Angle > 45. No.
From Pan (10, 4) facing North/East?
No.
So A is definitely unobserved.

One edge case: "Door blocks vision... Exception: When located in a doorway...".
I was at Green Door.
Did I see A?
Green Door position is the key.
If Green Door is at (7, 4).
Then A (9, 4) is (2, 0) from Door.
Angle 0.
Visible!
Is Green Door at (7, 4)?
Pan (10, 4).
From Pan facing North, Door is "Front-Left".
From (10, 4), Door (7, 4) is Vector (-3, 0). West.
Angle 90 deg Left.
Bin: [-45, -22.5) is front-left.
Left (90) is NOT front-left.
So Door cannot be at (7, 4).
So A was NOT seen from Door.

Conclusion stands: A is unobserved. B is observed.

Final Answer seems to be A.
However, I will verify if "candidates" implies I should look for *any* labelled points.
Usually I select from the labels.
If I select A, it is ["A"].

Wait, if B is "candidates" and "unexplored", maybe "unexplored" means "not visited"?
"Unexplored/unobserved".
I visited Pan (10,4). B is (9,3). I did not visit B.
But "unobserved" is the criteria.
B was observed (in FOV).
So B is not unobserved.
A was not observed.
So A is the answer.

FINAL ANSWER:
{
"unexplored": ["A"]
}

THINK:
I have successfully found the missing object, the 'laptop', by rotating to face South in Room 3.
Now I need to address the Fog Probe task.
The map provided shows a grid layout.
Room 1 is likely the top-left section (connecting via a door on its South wall to Room 2? No, let's trace coordinate...

###############
#......########
#......########
#......########
#......########
#......########
#......########
######+########
#......########
#......+......#
#......#......#
#......#A*....#
#......#B.....#
#......#......#
########......#
###############

You rotated clockwise 90°. You observe:
• laptop: front, near, facing left.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• laptop: front, near, facing left.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I have found the laptop! It was in Room 3, to the South of the pan.
I have now identified all 12 objects:
Room 1: TV, chair (No, chair is Room 2), truck (Room 3), bike, backpack (Room 2), pan (Room 3), cap, lamp, vase (Room 2), shelf (Room 3), rubberduck (Room 2), laptop (Room 3).
Wait, let me double check the list.
1: television (Room 1)
2: chair (Room 2)
3: truck (Room 3)
4: bike (Room 1)
5: backpack (Room 2)
6: pan (Room 3)
7: cap (Room 1)
8: lamp (Room 1)
9: vase (Room 2)
10: shelf (Room 3)
11: rubberduck (Room 2)
12: laptop (Room 3)

I have observed all objects and connected all rooms.
Room 1: Start -> Blue Door -> Green Door.
Room 2: Blue Door -> Vase area.
Room 3: Green Door -> Pan area -> Laptop.
I have established spatial relationships for all items.
I am confident I have a complete map.
I can now terminate the exploration.

I have found the laptop! It was in Room 3, to the South of the pan.
I have now identified all 12 objects:
Room 1: TV, chair (No, chair is Room 2), truck (Room 3), bike, backpack (Room 2), pan (Room 3), cap, lamp, vase (Room 2), shelf (Room 3), rubberduck (Room 2), laptop (Room 3).
Wait, let me doubl...

THINK:
I need to reconstruct the global map based on the sequence of observations and movements.

**Initial State:**
- Agent at (0, 0), facing North.
- Observed:
- `bike`: front-right (NE), mid distance (approx 2-4m). Let's estimate (2, 2) or (2, 3). Facing left (West).
- `lamp`: front (N), mid distance (2-4m). Let's estimate (0, 3).
- `blue door`: front-right, slightly far (4-8m), on front wall. Since it's on the front wall (North), and slightly far, maybe y=5 or 6? Let's say (2, 5). Note: "on front wall" implies the wall is North. The door is an opening.

**Step 1:** JumpTo(blue door), Rotate(180).
- Agent at `blue door` (approx 2, 5). Facing South.
- Observed:
- `television`: front-right (SW), slightly far. Facing left (East). Relative to (2, 5) facing South, front-right is West/South-West.
- `cap`: front-slight-right (S/SW), slightly far. Facing left (East).
- `green door`: front-left (SE), mid distance, on left wall. Left wall facing South is East wall. So green door is East. Let's say at (5, 2) or (6, 3).
- Relation: `television` is east, near to `cap`. Wait. If TV is East of Cap, and both are generally West of the agent (facing South), then Cap is further West.
- Let's refine coordinates.
- Blue door is at (x_bd, y_bd). Agent facing South (-y).
- Green door is on East wall.
- TV and Cap are in Room 1.
- Previous view (from 0,0 facing N): Bike (NE), Lamp (N).
- Blue door (2, 5).
- Facing South from (2, 5):
- Green door (East wall): Front-Left. S -> Left is East. Correct. Mid distance (~3-4). Position approx (5, 2).
- TV: Front-Right. S -> Right is West. So TV is West of (2, 5). Maybe (-1, 3).
- Cap: Front-Slight-Right. Near TV.
- Relation: "television is east, near to cap". So Cap is West of TV. e.g. Cap (-3, 3), TV (-1, 3).
- TV facing Left (East). Cap facing Left (East).

**Step 2:** Rotate(180).
- Agent at `blue door` (2, 5). Facing North (into Room 2).
- Observed:
- `vase`: front-left (NW), slightly far.
- `rubberduck`: front-slight-left (NW), slightly far. Facing left (West).

**Step 3:** JumpTo(vase), Rotate(180).
- Agent at `vase`. Let's estimate vase position. From (2, 5) facing N, front-left is NW. Distance slightly far (~5). Say (-2, 9).
- Facing South.
- Observed:
- `chair`: front-left (SE relative to vase), slightly far. Facing left (East).
- `backpack`: front (S), near. Facing forward (South).
- `blue door`: front-left (SE), slightly far, on front wall. This matches. Vase is NW of door. Door is SE of vase.
- Refined Room 2:
- Vase (-2, 9).
- Rubberduck was front-slight-left from door. Near vase? From door (2,5) N: duck is NW.
- From Vase (-2, 9) S: Duck not seen? (Maybe behind or outside FOV).
- Chair is front-left (SE of vase). Maybe (1, 7). Facing East.
- Backpack is front (S of vase). Near (~2). (-2, 7). Facing South.

**Step 4:** JumpTo(blue door), JumpTo(green door), Rotate(-90).
- Agent at `green door`. Estimate (5, 2). Facing East (into Room 3).
- Observed:
- `truck`: front-right (SE), slightly far. Facing backward (West).
- `pan`: front-right (SE), mid distance. Facing forward (East).
- `shelf`: front-right (SE), slightly far.
- Relation: `truck` is north, near to `pan`.
- From (5, 2) facing East:
- Front-Right is SE.
- Pan is mid (~3). Say (7, -1).
- Truck is North of Pan. Say (7, 0).
- Shelf is SE. Say (8, -2).

**Step 5:** JumpTo(pan), Rotate(-90).
- Agent at `pan` (7, -1). Facing North.
- Observed:
- `green door`: front-left (NW). Correct. Door is (5, 2). Pan is (7, -1). Relative: Door is (-2, +3). NW. Matches.

**Step 6:** Rotate(90).
- Agent at `pan` (7, -1). Facing East.
- Observed:
- `truck`: front (E). Wait. Previously "truck is north, near to pan".
- If I am at Pan facing East, North is my Left.
- Observation says: `truck`: front, near.
- Contradiction?
- Step 4 says: "truck is north, near to pan".
- Step 6 says: At Pan, facing East, Truck is Front (East).
- Let's check "Facing backward" description of truck in Step 4.
- Let's trust the relative report "truck is north, near to pan" from Step 4 over the "front" from Step 6? Or maybe Step 6 is more direct.
- Step 6: "truck: front, near".
- Step 4: "truck: front-right... truck is north, near to pan".
- If Truck is East of Pan, then from Door (5, 2) facing East:
- Pan (7, -1) is SE.
- Truck (9, -1) is SE.
- Is Truck North of Pan? No, same Y.
- Is Truck near Pan? Yes.
- Let's re-read Step 4 relative report. "Assume your current facing direction is called 'north' [which is East]: truck is north [relative North = global East], near to pan."
- Ah! The relative report in Step 4 uses the *agent's facing direction* (East) as "north". So "truck is north" relative to agent means Truck is in the direction the agent is facing (East).
- So Truck is East of Pan.
- This matches Step 6 (Facing East -> Truck is Front).
- OK. Pan at (7, -1). Truck at (9, -1).
- Shelf: front-right (SE from Pan?). In Step 6 facing East, Shelf is front-right (SE). Matches.
- Shelf at (9, -3).

**Step 7:** Rotate(90).
- Agent at `pan` (7, -1). Facing South.
- Observed:
- `laptop`: front (S), near. Facing left (East).
- So Laptop is South of Pan. (7, -3).

**Refined Coordinate Estimation:**

*Room 1 (Origin 0,0)*
- Agent start (0,0).
- `lamp`: North of (0,0). (0, 3).
- `bike`: NE of (0,0). (2, 2). Facing West.
- `blue door`: North wall. (2, 5).
- `green door`: East wall. (5, 2).
- `television`: From door (2,5) facing S, it's Front-Right (SW). W of agent. (-2, 3). Facing East.
- `cap`: Near TV, West of TV? Step 1 said "TV is east, near to cap". So Cap is West. (-4, 3). Facing East.

*Room 2 (Connected via Blue Door at 2,5)*
- North of Blue Door.
- `vase`: NW of Door. (-1, 8).
- `rubberduck`: Near Vase. From Door facing N, it's slight-left. (-1, 7). Facing West.
- `chair`: From Vase (-1, 8) facing S, it's Front-Left (SE). (1, 6). Facing East.
- `backpack`: From Vase (-1, 8) facing S, it's Front (S). (-1, 6). Facing South.

*Room 3 (Connected via Green Door at 5,2)*
- East of Green Door.
- `pan`: SE of Door. (7, -1). Facing East.
- `truck`: East of Pan. (9, -1). Facing West (Step 4 said facing backward relative to agent facing East? No, Step 4 said "facing backward". Agent was East. Backward is West. Matches).
- `shelf`: SE of Pan. (9, -3).
- `laptop`: South of Pan. (7, -3). Facing East.

**Final Coordinate List:**
- Agent (Final): at `pan` (7, -1) or `laptop`? No, last move was Rotate. Position is `pan` (7, -1). Facing South.
- `lamp`: (0, 3)
- `bike`: (2, 2), facing "west"
- `blue door`: (2, 5)
- `green door`: (5, 2)
- `television`: (-2, 3), facing "east"
- `cap`: (-4, 3), facing "east"
- `vase`: (-1, 8)
- `rubberduck`: (-1, 7), facing "west"
- `chair`: (1, 6), facing "east"
- `backpack`: (-1, 6), facing "south"
- `pan`: (7, -1), facing "east"
- `truck`: (9, -1), facing "west"
- `shelf`: (9, -3)
- `laptop`: (7, -3), facing "east"

Let's double check coordinates vs "Slightly Far" etc.
- Door (2,5) to Vase (-1, 8): dx=3, dy=3. Dist = sqrt(18) = 4.2. "Slightly far" (4-8). Fits.
- Vase (-1, 8) to Backpack (-1, 6): dist 2. "Near" (0-2]. Fits.
- Door (5, 2) to Pan (7, -1): dx=2, dy=3. Dist = 3.6. "Mid distance" (2-4). Fits.
- Pan (7, -1) to Truck (9, -1): dist 2. "Near" (0-2]. Fits.
- Pan (7, -1) to Laptop (7, -3): dist 2. "Near". Fits.

Looks consistent.

FINAL ANSWER:
```json
{
"agent": {"position": [7, -1], "facing": "south"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"blue door": {"position": [2, 5]},
"green door": {"position": [5, 2]},
"television": {"position": [-2, 3], "facing": "east"},
"cap": {"position": [-4, 3], "facing": "east"},
"vase": {"position": [-1, 8]},
"rubberduck": {"position": [-1, 7], "facing": "west"},
"chair": {"position": [1, 6], "facing": "east"},
"backpack": {"position": [-1, 6], "facing": "south"},
"pan": {"position": [7, -1], "facing": "east"},
"truck": {"position": [9, -1], "facing": "west"},
"shelf": {"position": [9, -3]},
"laptop": {"position": [7, -3], "facing": "east"}
}
```

THINK:
I need to reconstruct the global map based on the sequence of observations and movements.

**Initial State:**
- Agent at (0, 0), facing North.
- Observed:
- `bike`: front-right (NE), mid distance (approx 2-4m). Let's estimate (2, 2) or (2, 3). Facing left (West).
- `lamp`: front (N), mid ...

{
  "agent": {
    "position": [
      7,
      -1
    ],
    "facing": "south"
  },
  "lamp": {
    "position": [
      0,
      3
    ]
  },
  "bike": {
    "position": [
      2,
      2
    ],
    "facing": "west"
  },
  "blue door": {
    "position": [
      2,
      5
    ]
  },
  "green door": {
    "position": [
      5,
      2
    ]
  },
  "television": {
    "position": [
      -2,
      3
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      -4,
      3
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      -1,
      8
    ]
  },
  "rubberduck": {
    "position": [
      -1,
      7
    ],
    "facing": "west"
  },
  "chair": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      6
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      9,
      -1
    ],
    "facing": "west"
  },
  "shelf": {
    "position": [
      9,
      -3
    ]
  },
  "laptop": {
    "position": [
      7,
      -3
    ],
    "facing": "east"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      2,
      -1
    ],
    "facing": "east"
  },
  "chair": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      10,
      1
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      2,
      3
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  },
  "pan": {
    "position": [
      8,
      1
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      4,
      -1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      0,
      4
    ],
    "facing": "east"
  },
  "vase": {
    "position": [
      0,
      11
    ],
    "facing": "east"
  },
  "shelf": {
    "position": [
      12,
      -1
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      4,
      11
    ],
    "facing": "west"
  },
  "laptop": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      6,
      3
    ],
    "facing": "east"
  },
  "blue door": {
    "position": [
      5,
      5
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      8,
      1
    ],
    "facing": "south"
  }
}

You have returned to the initial position and face north.
There are 4 objects in the room that have been changed (position or orientation).
Note one object is either moved or rotated, not both.
Goal: Explore the room again and identify which objects have been changed and how with minimum costs.
Use the same action set as the exploration phase.
You must use the Term(changes="...") action to submit your answer and terminate.
Format: Term(changes="object1: change_type, object2: change_type")
Example: Term(changes="apple: position, chair: orientation")
You have a maximum of 15 steps.

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

You have returned to the initial position and face north.
There are 4 objects in the room that have been changed (position or orientation).
Note one object is either moved or rotated, not both.
Goal: Explore the room again and identify which objects have been changed and how with minimum costs.
Use ...

I am back in Room 1 at the initial position (0,0) facing North. The environment is the same layout (3 rooms), but 4 objects have changed (either position or orientation). I need to re-visit the rooms and check the objects against my memory/map from the first phase to identify the changes.

My previous map state (Phase 1 summary):
Room 1:
- Start (0,0) facing North.
- Saw: bike (front-right, mid, facing left), lamp (front, mid), blue door (front-right, slightly far).
- From Blue Door facing South: TV (front-right, slightly far, facing left), cap (front-slight-right, slightly far, facing left), green door (left wall).
- Relationships: TV is East of Cap? No, wait. Facing South. Front-Right is West. So TV and Cap are West.
- Let's verify Room 1 objects: Bike, Lamp, TV, Cap.

Room 2:
- From Blue Door facing North: Vase (front-left, slightly far), Rubberduck (front-slight-left, slightly far, facing left).
- From Vase facing South: Chair (front-left, slightly far, facing left), Backpack (front, near, facing forward).

Room 3:
- From Green Door facing East: Truck (front-right, slightly far, facing backward), Pan (front-right, mid, facing forward), Shelf (front-right, slightly far).
- From Pan facing East: Truck (front, near, facing backward), Shelf (front-right).
- From Pan facing South: Laptop (front, near, facing left).

Plan:
1. Observe Room 1 from current position. Check Bike and Lamp.
2. Jump to Blue Door. Check TV and Cap (Rotate 180).
3. Check Room 2. Rotate 180 to face North. Check Vase, Rubberduck.
4. Jump to Vase (or just observe if clear). Check Chair, Backpack.
5. Go to Room 3 (via Green Door). Check Truck, Pan, Shelf, Laptop.

Step 1: Observe current view.
I expect to see:
- Bike: front-right, mid dist, facing left.
- Lamp: front, mid dist.
- Blue door: front-right.

I am back in Room 1 at the initial position (0,0) facing North. The environment is the same layout (3 rooms), but 4 objects have changed (either position or orientation). I need to re-visit the rooms and check the objects against my memory/map from the first phase to identify the changes.

My previo...

THINK:
I have re-observed the initial view in Room 1.
Observations:
- `bike`: front-right, mid, facing left. Matches previous (Room 1).
- `lamp`: front, mid. Matches previous (Room 1).
- `blue door`: front-right, on front wall. Matches previous.
- `laptop`: front-slight-right, slightly far, facing right. **CHANGE DETECTED**.
- In Phase 1, the `laptop` was in Room 3 (found south of the pan).
- Now it is in Room 1.
- This is a **Position** change for the `laptop`.

Wait, the prompt asks for a "Cognitive Map (JSON)" output now.
I need to reconstruct the coordinates based on my exploration history.
Initial position: (0,0), facing North.

Phase 1 Reconstruction:
- Start (0,0) facing N.
- Blue door (front-right). Let's estimate coords.
- Bike (front-right).
- Lamp (front).
- Jump to Blue Door. Let's say Blue Door is at (2, 5).
- Rotate 180 (Face S).
- Green Door (left wall -> East). Let's say at (5, 4).
- TV (front-right -> West).
- Cap (front-slight-right -> West).
- Jump to Green Door (5, 4).
- Room 3 is to the East.
- Pan was mid distance.
- Laptop was south of Pan.
- Jump to Vase (Room 2).
- Room 2 is North of Room 1 (via Blue Door).
- Vase (front-left from Blue Door facing N). West side.

Let's refine coordinates relative to (0,0).
Room 1 (approx 5x5?):
- Agent (0,0).
- Lamp: Front (N). Maybe (0, 3).
- Bike: Front-Right (NE). Maybe (2, 2).
- Blue Door: Front-Right, slightly far. Maybe (2, 5) or (3, 6). "On front wall". Let's assume North wall.
- Laptop (New): Front-slight-right, slightly far. Maybe (1, 4).

Room 2 (North of Blue Door):
- Blue Door at (3, 6).
- Vase: Front-Left (NW). Maybe (0, 9).
- Rubberduck: Front-slight-left. Maybe (1, 9).
- Chair: From Vase (S) -> Front-Left (SE). Maybe (2, 7).
- Backpack: From Vase (S) -> Front (S). Maybe (0, 7).

Room 3 (East of Green Door):
- Green Door is on "left wall" of Room 1 (facing S). So East wall. Let's say (6, 2).
- Jump to Green Door. Face East.
- Pan: Front-right (SE). Maybe (8, 0).
- Truck: Front-right. Maybe (9, -1).
- Shelf: Front-right. Maybe (9, 1).
- Laptop (Old): South of Pan. Maybe (8, -2).
- Laptop (New): Moved to Room 1.

Current Observations (Phase 2, Step 1):
- Agent at (0,0) facing North.
- Bike: (2, 2) facing West (Left).
- Lamp: (0, 3).
- Blue Door: (3, 6).
- Laptop: (1, 4) facing East (Right).

Changes Identified so far:
1. `laptop`: Changed Position (Room 3 -> Room 1).

I need to check the other objects.
- Room 1: TV, Cap, Green Door. (Need to check orientation/pos).
- Room 2: Vase, Duck, Chair, Backpack.
- Room 3: Truck, Pan, Shelf. (Laptop is gone).

Let's create the JSON map with current best estimates.
I will use approximate integer coordinates that fit the "bins".
"Mid distance" (2, 4]. "Slightly far" (4, 8].
- Lamp: Front, mid. (0, 3).
- Bike: Front-right, mid. (2, 2).
- Laptop (New): Front-slight-right, slightly far. (1, 5).
- Blue Door: Front-right, slightly far. (3, 6).
- Green Door: From Blue Door (3,6) facing S, it's Front-Left (East). Mid distance. (6, 3).
- TV: From Blue Door facing S, Front-Right (West). Slightly far. (-1, 3).
- Cap: From Blue Door facing S, Front-slight-Right (West). Slightly far. (0, 2).

Room 2:
- Vase: From Blue Door facing N, Front-Left. Slightly far. (0, 9).
- Rubberduck: Front-slight-left. Slightly far. (1, 9).
- Chair: From Vase (0,9) facing S, Front-Left (SE). Slightly far. (3, 7).
- Backpack: From Vase facing S, Front (S). Near. (0, 7).

Room 3:
- Pan: From Green Door (6,3) facing E, Front-Right (SE). Mid. (8, 1).
- Truck: From Green Door facing E, Front-Right (SE). Slightly far. (9, 0).
- Shelf: From Green Door facing E, Front-Right (SE). Slightly far. (9, 2).

This looks like a reasonable map.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"},
"blue door": {"position": [3, 6], "facing": "north"},
"green door": {"position": [6, 3], "facing": "east"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 2], "facing": "west"},
"laptop": {"position": [1, 5], "facing": "east"},
"television": {"position": [-1, 3], "facing": "east"},
"cap": {"position": [0, 2], "facing": "east"},
"vase": {"position": [0, 9]},
"rubberduck": {"position": [1, 9], "facing": "west"},
"chair": {"position": [3, 7], "facing": "east"},
"backpack": {"position": [0, 7], "facing": "north"},
"pan": {"position": [8, 1], "facing": "north"},
"truck": {"position": [9, 0], "facing": "south"},
"shelf": {"position": [9, 2]}
}
```

THINK:
I have re-observed the initial view in Room 1.
Observations:
- `bike`: front-right, mid, facing left. Matches previous (Room 1).
- `lamp`: front, mid. Matches previous (Room 1).
- `blue door`: front-right, on front wall. Matches previous.
- `laptop`: front-slight-right, slightly far, facing r...

You observe:
• bike: front-right, mid distance, facing left
• lamp: front, mid distance
• laptop: front-slight-right, slightly far, facing right
• blue door: front-right, slightly far, on front wall
Assume your current facing direction is called "north":
• bike is south east, near to laptop
• lamp is west, near to laptop.
You have a maximum of 14 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You observe:
• bike: front-right, mid distance, facing left
• lamp: front, mid distance
• laptop: front-slight-right, slightly far, facing right
• blue door: front-right, slightly far, on front wall
Assume your current facing direction is called "north":
• bike is south east, near to laptop
• lamp ...

Current Observation (Room 1, facing North):
- **Bike**: front-right, mid, facing left. (Matches Phase 1: bike: front-right, mid, facing left). Status: Unchanged.
- **Lamp**: front, mid. (Matches Phase 1: lamp: front, mid). Status: Unchanged.
- **Laptop**: front-slight-right, slightly far, facing right.
- Wait! In Phase 1, the **Laptop** was found in **Room 3** (South of the Pan).
- Now it is in **Room 1**.
- Change Detected: **Laptop: position**.
- **Blue door**: front-right. Unchanged.

I have found 1 change (Laptop moved to Room 1). I need to find 3 more changes.
I need to check the rest of Room 1 (TV, Cap) and then Room 2 and Room 3.
The laptop being here might mean something else was moved out, or just a swap.
Objects to check:
- Room 1: TV, Cap.
- Room 2: Vase, Rubberduck, Chair, Backpack.
- Room 3: Truck, Pan, Shelf (Laptop is already found).

Next Step: Check the rest of Room 1.
I need to see the TV and Cap. They were visible from the Blue Door facing South.
So, Jump to Blue Door, Rotate 180 (to face South), Observe.

Current Observation (Room 1, facing North):
- **Bike**: front-right, mid, facing left. (Matches Phase 1: bike: front-right, mid, facing left). Status: Unchanged.
- **Lamp**: front, mid. (Matches Phase 1: lamp: front, mid). Status: Unchanged.
- **Laptop**: front-slight-right, slightly far, facing rig...

THINK:
I am constructing the Global Cognitive Map based on my observations.
Origin (0,0) is my start position facing North.

**Room 1:**
- **Agent Start**: [0,0], facing North.
- **Lamp**: Front (North) of start, mid distance (~3-4 units). Let's estimate (0, 3). No facing info provided in first obs, but "facing left" for bike etc. Lamp usually has no facing or "facing ?". Prompt said "lamp: front, mid distance". No facing given. I will omit facing if not given.
- **Bike**: Front-right (NE), mid distance (~3-4 units). Facing Left (West). Estimate (2, 3).
- **Blue Door**: Front-right, slightly far (~5-6 units). On front wall (North wall). Let's place it at (2, 5).
- **Laptop**: Observed in Room 1 (Phase 2), front-slight-right, slightly far. Near lamp (West) and bike (SE). If lamp is (0,3) and bike is (2,3), laptop is "front-slight-right" from (0,0). "Slightly far" > 4. Maybe (1, 5)? Facing Right (East).

- **From Blue Door (2,5) facing South:**
- **Television**: Front-right (West relative to South -> West). Slightly far. Facing Left (North relative to global? Wait. "facing left" relative to agent facing South -> Agent's left is East. So TV facing East? Or "facing left" is egocentric? Usually prompts imply absolute facing "facing left" = West? Or relative?
- Re-reading instructions: "Orientation: forward/backward/right/left (ego)..." "When agent faces north: forward = north, right = east...".
- Report says "television: ... facing left". If I am facing South, "left" is East. So TV faces East?
- Wait, in Phase 1: "television: ... facing left". I was facing South. So facing East.
- Position: Front-right from South-facing door. Front = South. Right = West. So TV is South-West of door. Door at (2,5). TV at (-1, 1)?
- **Cap**: Front-slight-right. Slightly far. Facing backward.
- From South-facing door: Front-slight-right is South-South-West. Cap at (1, 2)? Facing backward relative to agent (facing South) -> Facing North.
- **Green Door**: Front-left (East relative to South -> East). Mid distance. On left wall. So on East wall. Position maybe (5, 2)?

**Room 2:**
- Connected via Blue Door (2, 5). Room 2 is North of Room 1.
- From Blue Door facing North:
- **Vase**: Front-left (NW). Slightly far. Estimate (-1, 8).
- **Rubberduck**: Front-slight-left. Slightly far. Facing left (West). Estimate (0, 9).
- **Chair**: Observed from Vase facing South. "Front-left" (East relative to South -> East). Slightly far. From (-1, 8) facing South, East is towards +x. Maybe (2, 7)? Facing Left (East relative to South -> East).
- **Backpack**: From Vase facing South. "Front" (South). Near. Facing forward (South). Maybe (-1, 6).

**Room 3:**
- Connected via Green Door (5, 2). Room 3 is East of Room 1.
- From Green Door facing East:
- **Truck**: Front-right (SE). Slightly far. Facing backward (West relative to East -> West). Estimate (8, -1).
- **Pan**: Front-right. Mid. Facing forward (East). Estimate (7, 0).
- **Shelf**: Front-right. Slightly far. Estimate (8, -2).
- **Laptop** (Phase 1 position): South of Pan. Now moved to Room 1.

**Changes Detected so far:**
1. **Laptop**: Moved from Room 3 to Room 1.
2. **Cap**: Phase 1: "facing left" (East). Phase 2: "facing backward" (North). Change: **Orientation**.
3. **Television**: Phase 1: "facing left". Phase 2: "facing left". Unchanged.

I need to map the coordinates more consistently.
Let's refine:
- Agent at (0,0).
- Blue Door at (0, 5) or similar. "Front-right" from (0,0) -> (2, 5) is okay.
- Green Door at (5, 0) or similar. "Front-left" from Blue Door facing South (2, 5). Facing South, Front is -y. Left is +x. So Green Door is at roughly (5, 2).
- Laptop (Phase 2): Front-slight-right from (0,0). Near Lamp/Bike.
- Cap (Phase 2): Front-slight-right from Blue Door facing South. (South-West). Facing Backward (North).

Let's verify positions for JSON:
- Lamp: (0, 3).
- Bike: (2, 3). Facing West.
- Laptop: (1, 4). Facing East.
- Blue Door: (2, 5).
- Green Door: (5, 2).
- TV: (-1, 1). Facing East.
- Cap: (1, 2). Facing North.
- Vase: (-1, 8).
- Rubberduck: (0, 9). Facing West.
- Chair: (2, 7). Facing East.
- Backpack: (-1, 6). Facing South.
- Truck: (8, -1). Facing West.
- Pan: (7, 0). Facing East.
- Shelf: (8, -2).

Wait, I need to finalize the JSON. The coordinates don't have to be perfect, just topologically reasonable.
I will assume standard integer grid logic.
Objects to include: television, chair, truck, bike, backpack, pan, cap, lamp, vase, shelf, rubberduck, laptop, blue door, green door, agent.

Change check:
- Laptop: Position (Room 3 -> Room 1).
- Cap: Orientation (East -> North).
- Need to find 2 more.

JSON Output:
Agent at (2, 5) facing South (from last action).
Wait, last action was `JumpTo(blue door), Rotate(180), Observe()`.
So I am at Blue Door (2, 5), facing South.

FINAL ANSWER:
```json
{
"agent": {"position": [2, 5], "facing": "south"},
"blue door": {"position": [2, 5], "facing": "north"},
"green door": {"position": [5, 2], "facing": "east"},
"lamp": {"position": [0, 3]},
"bike": {"position": [2, 3], "facing": "west"},
"laptop": {"position": [1, 4], "facing": "east"},
"television": {"position": [-1, 1], "facing": "east"},
"cap": {"position": [1, 2], "facing": "north"},
"vase": {"position": [-1, 8]},
"rubberduck": {"position": [0, 9], "facing": "west"},
"chair": {"position": [2, 7], "facing": "east"},
"backpack": {"position": [-1, 6], "facing": "south"},
"truck": {"position": [8, -1], "facing": "west"},
"pan": {"position": [7, 0], "facing": "east"},
"shelf": {"position": [8, -2]}
}
```

THINK:
I am constructing the Global Cognitive Map based on my observations.
Origin (0,0) is my start position facing North.

**Room 1:**
- **Agent Start**: [0,0], facing North.
- **Lamp**: Front (North) of start, mid distance (~3-4 units). Let's estimate (0, 3). No facing info provided in first obs,...

You jumped to blue door. You rotated clockwise 180°. You observe:
• television: front-right, slightly far, facing left
• cap: front-slight-right, slightly far, facing backward
• green door: front-left, mid distance, on left wall
Assume your current facing direction is called "north":
• television is east, near to cap.
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 rotated clockwise 180°. You observe:
• television: front-right, slightly far, facing left
• cap: front-slight-right, slightly far, facing backward
• green door: front-left, mid distance, on left wall
Assume your current facing direction is called "north":
• television i...

I am at the Blue Door facing South (looking into Room 1).
Observations:
- **Television**: front-right, slightly far, facing left.
- Phase 1: front-right, slightly far, facing left.
- Match. Status: Unchanged.
- **Cap**: front-slight-right, slightly far, **facing backward**.
- Phase 1: front-slight-right, slightly far, **facing left**.
- Change Detected: **Cap: orientation**.
- **Green Door**: front-left. Unchanged.

So far:
1. Laptop: position (moved from Room 3 to Room 1).
2. Cap: orientation (changed from facing left to facing backward).

Remaining potential changes: 2.
Objects left to check:
- Room 2: Vase, Rubberduck, Chair, Backpack.
- Room 3: Truck, Pan, Shelf.

Next Step: Check Room 2.
I am at the Blue Door facing South. I need to turn around to face North into Room 2.
Rotate 180, Observe.

I am at the Blue Door facing South (looking into Room 1).
Observations:
- **Television**: front-right, slightly far, facing left.
- Phase 1: front-right, slightly far, facing left.
- Match. Status: Unchanged.
- **Cap**: front-slight-right, slightly far, **facing backward**.
- Phase 1: front-sl...

THINK:
I need to generate a global cognitive map of the current state based on my observations in Phase 1 and the changes detected in Phase 2.

**Phase 1 Recap & Coordinates Estimation:**
Agent starts at (0,0) facing North.
1. **Room 1 (Initial):**
* **Agent**: (0,0) facing North.
* **Lamp**: "front, mid distance". Mid is (2,4]. Let's estimate (0, 3).
* **Bike**: "front-right, mid distance, facing left". Front-right is ~45 deg. Dist ~3. Approx (2, 2). Facing Left = West.
* **Blue Door**: "front-right, slightly far". Slightly far is (4,8]. Let's say (3, 5). On "front wall" of Room 1.
* **Laptop (Phase 2)**: "front-slight-right, slightly far, facing right". Slightly far ~5. Slight right ~15 deg. Approx (1, 5). Facing Right = East. (Moved from Room 3).

2. **Room 1 (From Blue Door facing South):**
* Agent at Blue Door (3, 5). Facing South.
* **Television**: "front-right, slightly far". Facing South, front-right is West. Dist ~5. Maybe (-2, 0). Facing Left (relative to agent facing South) = East. Wait, "facing left" in description usually implies relative to agent? Or absolute? The instructions say "facing left (ego)". If agent faces South, left is East. So TV faces East.
* **Cap**: "front-slight-right, slightly far". Near TV. Maybe (-1, 1). Phase 1: facing left (East). Phase 2: facing backward (North).
* **Green Door**: "front-left, mid distance". Facing South, front-left is South-East. Wall is "left wall" (East wall). Let's say (6, 2).

3. **Room 2 (From Blue Door facing North):**
* Agent at Blue Door (3, 5). Facing North.
* **Vase**: "front-left, slightly far". Front-left is North-West. Dist ~5. (-1, 9).
* **Rubberduck**: "front-slight-left, slightly far, facing left". Dist ~6. (1, 10). Facing Left = West.
* **Missing from current view**: Vase? No, I only saw Rubberduck in the latest observation ("You observe: rubberduck..."). Wait. The prompt says "You observe: rubberduck...". It does NOT list the **vase**.
* **Change Detected**: **Vase is missing** from its original position. Or moved? I need to check if it moved or if I just can't see it. In Phase 1, I saw "vase: front-left, slightly far". Now I don't see it. It might be moved to a blind spot or another room. Or maybe "position" change implies it's gone from view.
* Also check inside Room 2.

4. **Room 2 (Inside, Phase 1 info):**
* Jumped to Vase. Rotated 180 (South). Saw **Chair**, **Backpack**.
* Chair: "front-left" (East-ish from Vase). Facing Left (East).
* Backpack: "front" (South from Vase). Facing Forward (South).

5. **Room 3 (Phase 1 info):**
* From Green Door (6, 2) facing East.
* **Truck**: "front-right". (South-East). Facing Backward (West).
* **Pan**: "front-right, mid". (South-East). Facing Forward (East).
* **Shelf**: "front-right".
* **Laptop (Phase 1)**: South of Pan. (Found in Phase 1, moved to Room 1 in Phase 2).

**Consolidated Map Construction:**
* **Agent**: Currently at Blue Door (approx 3, 5), facing North.
* **Blue Door**: (3, 5).
* **Green Door**: (6, 2).
* **Lamp**: (0, 3).
* **Bike**: (2, 2). Facing West.
* **Television**: (-2, 0). Facing East.
* **Cap**: (-1, 1). Facing North (Changed).
* **Laptop**: (1, 5). Facing East (Changed position from Room 3).
* **Rubberduck**: (1, 10). Facing West.
* **Vase**: **MISSING** from observation at Blue Door. Likely moved.
* **Chair**: Room 2. Approx (2, 8). Facing East.
* **Backpack**: Room 2. Approx (0, 7). Facing South.
* **Truck**: Room 3. Approx (8, 0). Facing West.
* **Pan**: Room 3. Approx (9, 0). Facing East.
* **Shelf**: Room 3. Approx (10, -1).

I need to be careful. The task asks for the *current* state.
Changes found:
1. Laptop (pos)
2. Cap (orient)
3. Vase (missing from view -> likely position change).

I haven't checked Room 3 yet in Phase 2.
I haven't checked inside Room 2 fully (just from door).
The map should reflect the objects I know. For objects I haven't re-observed, I should assume they are at their last known location unless I have evidence otherwise? No, the goal is to *identify* changes.
But the JSON output asks for the "Global Cognitive Map" of the scene. I should provide coordinates.
I will estimate coordinates based on "mid distance" ~3, "slightly far" ~6.

Coordinates (Origin 0,0):
Agent: (0,0) start.
Blue Door: (3, 6). (Right 3, Front 6).
Lamp: (0, 4).
Bike: (2, 2). Facing West.
Laptop (New): (1, 5). Facing East.
TV: (-2, 1). Facing East.
Cap: (-1, 2). Facing North.
Green Door: (6, 2).
Room 2 (North of Blue Door):
Rubberduck: (1, 10). Facing West.
Vase: Phase 1 was at (-2, 9). Now missing? Let's assume it moved.
Chair: (0, 8). Facing East.
Backpack: (-1, 7). Facing South.
Room 3 (East of Green Door):
Truck: (9, 0). Facing West.
Pan: (10, 1). Facing East.
Shelf: (11, 0).

Wait, I need to provide the map *now*.
I will list the objects with their best estimated positions.
If Vase is moved, and I haven't found it, I might list it at old pos or omit?
Actually, the instruction says "include ALL objects". I should probably list it where I think it is.
If I haven't found the Vase's new location, I can't map it accurately.
However, I must output a JSON.
I'll stick to the observed positions.
For objects not yet re-observed (Chair, Backpack, Truck, Pan, Shelf), I will use Phase 1 coordinates.
For Vase, since it's missing from view, and Laptop appeared in Room 1 (was Room 3), maybe Vase moved to Room 3? Or Room 1?
I didn't see Vase in Room 1.
I didn't see Vase in Room 2 view (only duck).
So Vase is likely in Room 2 (hidden) or Room 3.

Let's refine coordinates for consistency.
Agent start (0,0).
Lamp: (0,3).
Bike: (2,2).
Blue Door: (2,5).
TV: (-1, 1).
Cap: (0, 1).
Green Door: (5, 1).
Rubberduck: (1, 8).
Vase (Old): (-1, 8).
Chair: (-1, 7).
Backpack: (0, 6).
Truck: (8, 1).
Pan: (8, 0).
Shelf: (9, 0).
Laptop (New): (1, 4).

Let's standardize.
Door 1 (Blue): (3, 6).
Door 2 (Green): (6, 2).
Room 1 bounds: x[-4, 6], y[0, 6].
Room 2 bounds: x[-4, 6], y[6, 12].
Room 3 bounds: x[6, 12], y[-4, 6].

Objects:
1. Television: (-2, 1), facing East.
2. Chair: (-1, 9), facing East.
3. Truck: (9, 1), facing West.
4. Bike: (2, 2), facing West.
5. Backpack: (0, 8), facing South.
6. Pan: (9, 0), facing East.
7. Cap: (-1, 2), facing North.
8. Lamp: (0, 3).
9. Vase: (-2, 9). (Phase 1 pos). I haven't seen it yet in Phase 2.
10. Shelf: (10, 0).
11. Rubberduck: (1, 10), facing West.
12. Laptop: (1, 5), facing East. (New pos).

Blue Door: (3, 6).
Green Door: (6, 2).
Agent: Currently at Blue Door (3, 6), facing North.

FINAL ANSWER:
```json
{
"agent": {"position": [3, 6], "facing": "north"},
"television": {"position": [-2, 1], "facing": "east"},
"chair": {"position": [-1, 9], "facing": "east"},
"truck": {"position": [9, 1], "facing": "west"},
"bike": {"position": [2, 2], "facing": "west"},
"backpack": {"position": [0, 8], "facing": "south"},
"pan": {"position": [9, 0], "facing": "east"},
"cap": {"position": [-1, 2], "facing": "north"},
"lamp": {"position": [0, 3]},
"vase": {"position": [-2, 9]},
"shelf": {"position": [10, 0]},
"rubberduck": {"position": [1, 10], "facing": "west"},
"laptop": {"position": [1, 5], "facing": "east"},
"blue door": {"position": [3, 6]},
"green door": {"position": [6, 2]}
}
```

THINK:
I need to generate a global cognitive map of the current state based on my observations in Phase 1 and the changes detected in Phase 2.

**Phase 1 Recap & Coordinates Estimation:**
Agent starts at (0,0) facing North.
1. **Room 1 (Initial):**
* **Agent**: (0,0) facing North.
* **L...

You rotated clockwise 180°. You observe:
• rubberduck: front-slight-left, slightly far, facing left.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 180°. You observe:
• rubberduck: front-slight-left, slightly far, facing left.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am at the Blue Door facing North (looking into Room 2).
Observation:
- **Rubberduck**: front-slight-left, slightly far, facing left.
- Phase 1: front-slight-left, slightly far, facing left.
- Match. Status: Unchanged.
- **Vase**: NOT OBSERVED.
- Phase 1: Vase was "front-left, slightly far".
- If it's missing, it moved.
- Let me verify. In Phase 1, from Blue Door facing North, I saw "vase: front-left, slightly far" and "rubberduck...".
- Now I only see rubberduck.
- Possible change: **Vase: position** (moved to Room 3?).
- Or maybe it's just out of FOV due to a small shift? But "front-left" is usually quite visible. "Slightly far" is within range.
- It's likely moved.

I need to enter Room 2 to check the Chair and Backpack, and confirm the Vase is gone (or find it elsewhere).
I can jump to the Rubberduck to get inside.
Then turn to face South to see the Chair and Backpack.

Plan:
1. JumpTo(rubberduck).
2. Rotate(180) to face South.
3. Observe.

I am at the Blue Door facing North (looking into Room 2).
Observation:
- **Rubberduck**: front-slight-left, slightly far, facing left.
- Phase 1: front-slight-left, slightly far, facing left.
- Match. Status: Unchanged.
- **Vase**: NOT OBSERVED.
- Phase 1: Vase was "front-left, slightly far".
...

THINK:
I have explored Room 1 and Room 2 in the second phase.
Findings:
- **Room 1**:
- `bike`: Unchanged ([2, 2], West).
- `lamp`: Unchanged ([0, 3]).
- `laptop`: Moved to Room 1 ([1, 5], East). Previously in Room 3.
- `television`: Unchanged ([0, 2], East).
- `cap`: Rotated ([1, 2], North). Previously facing Left.
- **Room 2**:
- `rubberduck`: Unchanged ([1, 9], West).
- `chair`: Present ([0, 7], East).
- `vase`: Missing.
- `backpack`: Missing.
- **Room 3** (Not yet visited in Phase 2, relying on Phase 1 data + inference):
- `truck`: [8, 0], South.
- `pan`: [7, 1].
- `shelf`: [8, 2].
- Since `vase` and `backpack` are missing from Room 2 and not in Room 1, they are likely in Room 3.

I will generate the cognitive map based on these coordinates.

FINAL ANSWER:
```json
{
"agent": {"position": [1, 9], "facing": "south"},
"blue door": {"position": [2, 6], "facing": "north"},
"green door": {"position": [4, 3], "facing": "east"},
"bike": {"position": [2, 2], "facing": "west"},
"lamp": {"position": [0, 3]},
"laptop": {"position": [1, 5], "facing": "east"},
"television": {"position": [0, 2], "facing": "east"},
"cap": {"position": [1, 2], "facing": "north"},
"rubberduck": {"position": [1, 9], "facing": "west"},
"chair": {"position": [0, 7], "facing": "east"},
"truck": {"position": [8, 0], "facing": "south"},
"pan": {"position": [7, 1]},
"shelf": {"position": [8, 2]},
"vase": {"position": [6, 2]},
"backpack": {"position": [6, 4], "facing": "north"}
}
```

THINK:
I have explored Room 1 and Room 2 in the second phase.
Findings:
- **Room 1**:
- `bike`: Unchanged ([2, 2], West).
- `lamp`: Unchanged ([0, 3]).
- `laptop`: Moved to Room 1 ([1, 5], East). Previously in Room 3.
- `television`: Unchanged ([0, 2], East).
- `cap`: Rotated ([1, 2], Nort...

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

You jumped to rubberduck. You rotated clockwise 180°. You observe:
• chair: front-right, slightly far, facing left
• blue door: front-slight-left, slightly far, on front wall.
You have a maximum of 11 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
F...