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: bike, 2: airplane, 3: rubberduck, 4: lego man, 5: toilet, 6: truck, 7: backpack, 8: shoppingcart, 9: fridge, 10: soda can, 11: basket, 12: lamp
Doors: red door, green 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 ...

I am starting the exploration in Room 1 at position (0,0) facing North. The goal is to build a complete map of 3 rooms with minimal cost (Observe=1, Query=2) and limited steps (20). I currently have no visual information. My field of view is 90°. To systematically map Room 1 and find doors to the other rooms, I need to scan my surroundings. I will begin by observing the area directly in front of me (North).

I am starting the exploration in Room 1 at position (0,0) facing North. The goal is to build a complete map of 3 rooms with minimal cost (Observe=1, Query=2) and limited steps (20). I currently have no visual information. My field of view is 90°. To systematically map Room 1 and find doors to the ot...

THINK:
The agent is at [0, 0] facing North.
Observation: "lego man: front-left, slightly far, facing backward".
1. **Bearing**: "front-left" corresponds to [-45°, -22.5°). Taking the midpoint -33.75°.
2. **Distance**: "slightly far" corresponds to (4, 8]. Taking the midpoint 6.
3. **Coordinates**:
* x ≈ 6 * sin(-33.75°) ≈ -3.3
* y ≈ 6 * cos(-33.75°) ≈ 5.0
* Integer approximation: (-3, 5). Check: distance = √((-3)² + 5²) = √34 ≈ 5.83 (fits "slightly far"). Bearing = atan2(-3, 5) ≈ -31° (fits "front-left").
4. **Orientation**: Agent faces North. Object is "facing backward", which in the defined egocentric frame (where forward=north) means the object faces South.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"},
"lego man": {"position": [-3, 5], "facing": "south"}
}
```

THINK:
The agent is at [0, 0] facing North.
Observation: "lego man: front-left, slightly far, facing backward".
1. **Bearing**: "front-left" corresponds to [-45°, -22.5°). Taking the midpoint -33.75°.
2. **Distance**: "slightly far" corresponds to (4, 8]. Taking the midpoint 6.
3. **Coordinates**...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      5
    ],
    "facing": "south"
  }
}

{
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

THINK:
The agent is currently at the origin (0,0) facing North. The observation reports a "lego man" at "front-left" (bearing approx -33.75°) and "slightly far" (distance approx 6 units).
Using local coordinates where +y is forward (North) and +x is right (East):
x = 6 * sin(-33.75°) ≈ -3.3 ≈ -3
y = 6 * cos(-33.75°) ≈ 5.0 ≈ 5
The lego man is "facing backward", which corresponds to the -y direction in the local frame.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"lego man": {"position": [-3, 5], "facing": "-y"}
}
}
```

THINK:
The agent is currently at the origin (0,0) facing North. The observation reports a "lego man" at "front-left" (bearing approx -33.75°) and "slightly far" (distance approx 6 units).
Using local coordinates where +y is forward (North) and +x is right (East):
x = 6 * sin(-33.75°) ≈ -3.3 ≈ -3
y =...

{
  "origin": "agent",
  "objects": {
    "lego man": {
      "position": [
        -3,
        5
      ],
      "facing": "-y"
    }
  }
}

{
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  }
}

{
  "origin": "agent",
  "objects": {
    "lego man": {
      "position": [
        -3,
        5
      ],
      "facing": "-y"
    }
  }
}

{
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  }
}

THINK:
The agent is located at the position marked `*`. Based on the map structure and row counting:
- The agent `*` is at approximate coordinates (12, 5) (assuming bottom-left origin and counting lines).
- The agent is facing North (Up).
- The FOV is a 90° cone centered on North (45° to the left, 45° to the right).
- Candidates B, D, and E are located to the North of the agent.
- D (approx 13, 7) is within the cone (dx=1, dy=2).
- B (approx 11, 8) is within the cone (dx=-1, dy=3).
- E (approx 13, 8) is within the cone (dx=1, dy=3).
- Candidate A (approx 8, 7) is to the North-West.
- dx = 8 - 12 = -4. dy = 7 - 5 = 2.
- Since |dx| (4) > dy (2), point A is outside the 45° left boundary of the FOV. It is unobserved.
- Candidate C (approx 13, 4) is South of the agent (behind). It is unobserved.
- Candidate F (approx 8, 3) is South-West of the agent (behind). It is unobserved.

Therefore, the unexplored/unobserved points are A, C, and F.

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

THINK:
The agent is located at the position marked `*`. Based on the map structure and row counting:
- The agent `*` is at approximate coordinates (12, 5) (assuming bottom-left origin and counting lines).
- The agent is facing North (Up).
- The FOV is a 90° cone centered on North (45° to the left, 4...

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

You observe:
• lego man: front-left, slightly far, facing backward.
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:
• lego man: front-left, slightly far, facing backward.
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 observed the sector to my North. I see a lego man to the front-left. I need to continue scanning Room 1 to find the doors (red door, green door) and other objects. My current FOV is 90 degrees. I will rotate 90 degrees clockwise to face East and observe the next sector.

I have observed the sector to my North. I see a lego man to the front-left. I need to continue scanning Room 1 to find the doors (red door, green door) and other objects. My current FOV is 90 degrees. I will rotate 90 degrees clockwise to face East and observe the next sector....

THINK:
The agent is at [0,0] facing East.
From the first observation (facing North):
- Lego man was front-left (approx -30 deg) and slightly far (4-8m). Let's estimate coordinates. sin(-30)*6 = -3, cos(-30)*6 = 5. Position approx [-3, 5]. It was facing backward (South).

From the second observation (facing East):
- Green door is front (East) and near (0-2m). Let's estimate coordinates. x=2, y=0.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "east"},
"lego man": {"position": [-3, 5], "facing": "south"},
"green door": {"position": [2, 0]}
}
```

THINK:
The agent is at [0,0] facing East.
From the first observation (facing North):
- Lego man was front-left (approx -30 deg) and slightly far (4-8m). Let's estimate coordinates. sin(-30)*6 = -3, cos(-30)*6 = 5. Position approx [-3, 5]. It was facing backward (South).

From the second observation ...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  },
  "lego man": {
    "position": [
      -3,
      5
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  }
}

{
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "east"
  }
}

THINK:
I am currently facing East at (0,0). My last observation revealed a "green door" directly in front ("front") and "near". In the local frame (where +y is forward/East, +x is right/South), the green door is approximately at y=2, x=0. The previous object (lego man) was to the North-West (front-left when facing North) and is now likely out of my 90° field of view (East ± 45°). Therefore, I will only include the green door in the local map.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"green door": {"position": [0, 2]}
}
}
```

THINK:
I am currently facing East at (0,0). My last observation revealed a "green door" directly in front ("front") and "near". In the local frame (where +y is forward/East, +x is right/South), the green door is approximately at y=2, x=0. The previous object (lego man) was to the North-West (front-l...

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        0,
        2
      ]
    }
  }
}

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

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        0,
        2
      ]
    }
  }
}

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

THINK: [The agent is at position '*' facing East. Previous action was facing North. The agent has observed the Northern cone (up to 45 degrees left/right of North) and the Eastern cone (up to 45 degrees left/right of East).
- Candidate B is to the South. The agent has not looked South or West yet. So B is unobserved.
- Candidate D is to the West. The agent has not looked West. So D is unobserved.
- Candidate C is to the East, near the green door which was observed. So C is observed.
- Candidate E is directly North-West (dx=-1, dy=1 relative to agent). This falls on the 45-degree boundary of the North view. The agent observed a lego man 'front-left', which corresponds to this sector. E is likely observed.
- Candidate F is North-East. This falls within the North view. F is observed.
- Candidate A is further North-West (dx=-3, dy=2). The angle is approx 56 degrees left of North. The FOV is 45 degrees. Thus A is outside the North FOV cone. It is also outside the East FOV cone. So A is unobserved.]
FINAL ANSWER: { "unexplored": ["A", "B", "D"] }

THINK: [The agent is at position '*' facing East. Previous action was facing North. The agent has observed the Northern cone (up to 45 degrees left/right of North) and the Eastern cone (up to 45 degrees left/right of East).
- Candidate B is to the South. The agent has not looked South or West yet. ...

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

You rotated clockwise 90°. You observe:
• green door: front, near, on front wall.
You have a maximum of 18 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• green door: front, near, on front wall.
You have a maximum of 18 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I have found the green door in the East sector. I still need to scan South and West to complete the survey of Room 1 and potentially find the red door. I am currently facing East. I will rotate 90 degrees clockwise to face South and observe.

I have found the green door in the East sector. I still need to scan South and West to complete the survey of Room 1 and potentially find the red door. I am currently facing East. I will rotate 90 degrees clockwise to face South and observe....

THINK:
The agent is currently at [0, 0] facing South.
From previous steps:
1. **Face North:** "lego man" at front-left (NW), slightly far (dist ~5). Estimated position: [-3, 5]. "Facing backward" implies facing South.
2. **Face East:** "green door" at front (E), near (dist ~2). Estimated position: [2, 0].
3. **Face South:**
* "backpack" at front-right (SW), mid distance (dist ~3). Estimated position: [-2, -3]. "Facing forward" implies facing North.
* "shoppingcart" at front-left (SE), mid distance (dist ~3). Estimated position: [2, -3]. "Facing right" implies facing East.
* Proximity check: With local North = Global South, local East = Global West. "backpack is east ... to shoppingcart" means Backpack is West of Shoppingcart. This is consistent with Backpack at [-2, -3] and Shoppingcart at [2, -3].

FINAL ANSWER:
```json
{
"grid": {
"width": 20,
"height": 20
},
"agent": {
"position": [
0,
0
],
"facing": "south"
},
"lego man": {
"position": [
-3,
5
],
"facing": "south"
},
"green door": {
"position": [
2,
0
],
"facing": "east"
},
"backpack": {
"position": [
-2,
-3
],
"facing": "north"
},
"shoppingcart": {
"position": [
2,
-3
],
"facing": "east"
}
}
```

THINK:
The agent is currently at [0, 0] facing South.
From previous steps:
1. **Face North:** "lego man" at front-left (NW), slightly far (dist ~5). Estimated position: [-3, 5]. "Facing backward" implies facing South.
2. **Face East:** "green door" at front (E), near (dist ~2). Estimated position:...

{
  "grid": {
    "width": 20,
    "height": 20
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "south"
  },
  "lego man": {
    "position": [
      -3,
      5
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "north"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "east"
  }
}

{
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "south"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "south"
  }
}

THINK:
The agent is facing South.
Observations:
- Backpack: Front-right (relative East-ish), mid distance. Facing forward (relative North/Global South).
- Shoppingcart: Front-left (relative West-ish), mid distance. Facing right (relative East/Global West).
Relative Proximity Check: "backpack is east, near to shoppingcart". In the relative frame (where Agent Facing = North), "East" is Right. The Backpack is to the right (front-right) and the Shoppingcart is to the left (front-left), so Backpack is indeed "East" of the Shoppingcart in this relative frame.

Local Coordinates (Agent at 0,0, Facing +y):
- Backpack: Front-Right. x > 0, y > 0. Mid distance (2-4m). Let's estimate (2, 3). Facing: "+y" (Forward).
- Shoppingcart: Front-Left. x < 0, y > 0. Mid distance (2-4m). Let's estimate (-2, 3). Facing: "+x" (Right).

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"backpack": {"position": [2, 3], "facing": "+y"},
"shoppingcart": {"position": [-2, 3], "facing": "+x"}
}
}
```

THINK:
The agent is facing South.
Observations:
- Backpack: Front-right (relative East-ish), mid distance. Facing forward (relative North/Global South).
- Shoppingcart: Front-left (relative West-ish), mid distance. Facing right (relative East/Global West).
Relative Proximity Check: "backpack is east...

{
  "origin": "agent",
  "objects": {
    "backpack": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    },
    "shoppingcart": {
      "position": [
        -2,
        3
      ],
      "facing": "+x"
    }
  }
}

{
  "backpack": {
    "position": [
      1,
      2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      -1,
      2
    ],
    "facing": "west"
  }
}

{
  "origin": "agent",
  "objects": {
    "backpack": {
      "position": [
        2,
        3
      ],
      "facing": "+y"
    },
    "shoppingcart": {
      "position": [
        -2,
        3
      ],
      "facing": "+x"
    }
  }
}

{
  "backpack": {
    "position": [
      1,
      2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      -1,
      2
    ],
    "facing": "west"
  }
}

THINK: [The agent is located at the position marked `*`. Based on the map and the agent's observation history (North, East, South), I can determine which points have been within the 90° field of view. The agent is approximately at x=12 (relative to the left wall). The points F, E, and C are located to the north-left.
- **F (Row 6, Col 8)**: relative pos (-4, 1), angle ~-76°, outside North FOV (±45°).
- **E (Row 6, Col 10)**: relative pos (-2, 1), angle ~-63°, outside North FOV.
- **C (Row 5, Col 9)**: relative pos (-3, 2), angle ~-56°, outside North FOV.
- **A (Row 5, Col 11)**: relative pos (-1, 2), angle ~-26°, inside North FOV.
- **B (Row 5, Col 13)**: relative pos (1, 2), angle ~26°, inside North FOV.
- **D (Row 4, Col 9)**: relative pos (-3, 3), angle -45°, on the edge of North FOV. Given "lego man" was seen "slightly far" (dist ~4.24), D is likely observed.
Points A, B, and D are considered observed. Points C, E, and F are in the unobserved North-West region.]
FINAL ANSWER: { "unexplored": ["C", "E", "F"] }

THINK: [The agent is located at the position marked `*`. Based on the map and the agent's observation history (North, East, South), I can determine which points have been within the 90° field of view. The agent is approximately at x=12 (relative to the left wall). The points F, E, and C are located ...

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

You rotated clockwise 90°. You observe:
• backpack: front-right, mid distance, facing forward
• shoppingcart: front-left, mid distance, facing right
Assume your current facing direction is called "north":
• backpack is east, near to shoppingcart.
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 90°. You observe:
• backpack: front-right, mid distance, facing forward
• shoppingcart: front-left, mid distance, facing right
Assume your current facing direction is called "north":
• backpack is east, near to shoppingcart.
You have a maximum of 17 exploration steps left.
Str...

I have scanned North, East, and South.
North: Lego man.
East: Green door.
South: Backpack and shopping cart.
I need to scan the West sector to complete the initial sweep of Room 1 and look for the red door. I am currently facing South. I will rotate 90 degrees clockwise to face West and observe.

I have scanned North, East, and South.
North: Lego man.
East: Green door.
South: Backpack and shopping cart.
I need to scan the West sector to complete the initial sweep of Room 1 and look for the red door. I am currently facing South. I will rotate 90 degrees clockwise to face West and observe....

THINK:
I have completed a 360-degree scan of Room 1 from the starting position [0,0].
- Facing North, I saw a lego man in the NW quadrant facing South.
- Facing East, I saw a green door nearby at [2,0].
- Facing South, I saw a backpack in the SW quadrant facing South and a shopping cart in the SE quadrant facing West.
- Facing West, I saw a bike in the West/NW area facing South, confirmed the lego man's position, and saw a red door to the West at approximately [-5,0].

The map estimates are derived from the distance bins and bearings.
- Green door (East, near): [2, 0]
- Red door (West, slightly far): [-5, 0]
- Lego man (NW, slightly far): [-3, 3] facing South
- Bike (WNW, mid distance): [-3, 1] facing South
- Backpack (SW, mid distance): [-2, -2] facing South
- Shopping cart (SE, mid distance): [2, -2] facing West

I will output the JSON map.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "west"},
"green door": {"position": [2, 0]},
"red door": {"position": [-5, 0]},
"lego man": {"position": [-3, 3], "facing": "south"},
"bike": {"position": [-3, 1], "facing": "south"},
"backpack": {"position": [-2, -2], "facing": "south"},
"shoppingcart": {"position": [2, -2], "facing": "west"}
}
```

THINK:
I have completed a 360-degree scan of Room 1 from the starting position [0,0].
- Facing North, I saw a lego man in the NW quadrant facing South.
- Facing East, I saw a green door nearby at [2,0].
- Facing South, I saw a backpack in the SW quadrant facing South and a shopping cart in the SE qu...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "west"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      -2,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -2
    ],
    "facing": "west"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "west"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "west"
  }
}

THINK:
The agent is facing West. In the local frame, +y is West, +x is North.
Observed objects:
1. **bike**: "front-slight-right", "mid distance" (2-4m). "facing left".
* Position: Front-slight-right implies +y and +x. Let's estimate (1, 3).
* Facing: Left of West is South. In local frame (+y=West, +x=North), South is -x.
2. **lego man**: "front-right", "slightly far" (4-8m). "facing left".
* Position: Front-right implies +y and +x. Let's estimate (3, 5).
* Facing: Left of West is South (-x).
3. **red door**: "front", "slightly far" (4-8m).
* Position: Front implies +y, x=0. Let's estimate (0, 6).
* Facing: Not specified, usually aligned with wall.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"bike": {"position": [1, 3], "facing": "-x"},
"lego man": {"position": [3, 5], "facing": "-x"},
"red door": {"position": [0, 6]}
}
}
```

THINK:
The agent is facing West. In the local frame, +y is West, +x is North.
Observed objects:
1. **bike**: "front-slight-right", "mid distance" (2-4m). "facing left".
* Position: Front-slight-right implies +y and +x. Let's estimate (1, 3).
* Facing: Left of West is South. In local fra...

{
  "origin": "agent",
  "objects": {
    "bike": {
      "position": [
        1,
        3
      ],
      "facing": "-x"
    },
    "lego man": {
      "position": [
        3,
        5
      ],
      "facing": "-x"
    },
    "red door": {
      "position": [
        0,
        6
      ]
    }
  }
}

{
  "red door": {
    "position": [
      0,
      5
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  },
  "lego man": {
    "position": [
      3,
      3
    ],
    "facing": "south"
  }
}

{
  "origin": "agent",
  "objects": {
    "bike": {
      "position": [
        1,
        3
      ],
      "facing": "-x"
    },
    "lego man": {
      "position": [
        3,
        5
      ],
      "facing": "-x"
    },
    "red door": {
      "position": [
        0,
        6
      ]
    }
  }
}

{
  "red door": {
    "position": [
      0,
      5
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  }
}

You rotated clockwise 90°. You observe:
• bike: front-slight-right, mid distance, facing left
• lego man: front-right, slightly far, facing left
• red door: front, slightly far, on front wall
Assume your current facing direction is called "north":
• bike is west, near to lego man.
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

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

I have now completed a 360-degree scan of Room 1.
Findings:
- North (initial): Lego man (seen again from West view).
- East: Green door.
- South: Backpack, Shopping cart.
- West: Bike, Lego man, Red door.

I have found both doors connecting to other rooms. The red door is to the West, and the green door is to the East.
I should now explore the other rooms. I am currently facing West, looking at the red door. I will jump to the red door to see into the connected room (Room 2 or 3). Being in the doorway allows me to see both rooms, but I must orient myself to look into the new room. Since the red door is on the "front wall" relative to my current West facing, entering it means moving West. Once at the door, to look into the new room, I should look forward (West) relative to my arrival orientation, or perhaps look around.
However, the instruction says "When located in a doorway... you can see into both connected rooms."
Let's jump to the red door. My orientation will remain West. From the door, looking West should look into the new room. I will observe from there.

I have now completed a 360-degree scan of Room 1.
Findings:
- North (initial): Lego man (seen again from West view).
- East: Green door.
- South: Backpack, Shopping cart.
- West: Bike, Lego man, Red door.

I have found both doors connecting to other rooms. The red door is to the West, and the green ...

THINK:
I need to construct the JSON map based on my observations.
Initial State: Agent at (0,0), facing North.

1. **Step 1 (Face North):**
* Observed: `lego man` (front-left, slightly far). "Slightly far" is (4,8]. Let's estimate distance ~5 or 6. Front-left is approx -45 to -22.5 deg. In (x,y), North is +y. Front-left is North-West.
* Coordinates: If Agent is at (0,0) facing N, Lego man is roughly (-3, 5).

2. **Step 2 (Face East):**
* Rotated 90 deg clockwise. Now facing East (+x).
* Observed: `green door` (front, near). "Near" is (0,2]. Front is East.
* Coordinates: Green door is roughly at (2, 0).

3. **Step 3 (Face South):**
* Rotated 90 deg clockwise. Now facing South (-y).
* Observed: `backpack` (front-right, mid). Mid is (2,4]. Front-right (relative to South) is South-West.
* Observed: `shoppingcart` (front-left, mid). Front-left (relative to South) is South-East.
* Coordinates: Backpack roughly (-2, -3). Shoppingcart roughly (2, -3).

4. **Step 4 (Face West):**
* Rotated 90 deg clockwise. Now facing West (-x).
* Observed: `bike` (front-slight-right, mid). Mid is (2,4]. Front-slight-right relative to West is West-North-West.
* Observed: `lego man` (front-right, slightly far). Confirms previous sighting. Front-right relative to West is North-West. Consistent.
* Observed: `red door` (front, slightly far). Slightly far is (4,8]. Front is West.
* Coordinates: Red door roughly (-5, 0). Bike roughly (-3, 1).

5. **Step 5 (Jump to red door):**
* Agent position is now `red door` position (-5, 0).
* Orientation: West.
* Observed (looking West into new room):
* `rubberduck` (front-slight-right, slightly far). Front (West) + Right = West-North. Dist ~5. Pos: (-10, 2).
* `truck` (front-right, mid). Front (West) + Right = North-West. Dist ~3. Pos: (-7, 2).
* `lamp` (front-right, slightly far). West + Right = North-West. Dist ~5. Pos: (-8, 4).

Wait, let's refine coordinates based on "front-right" bins.
From (-5,0) facing West:
Front is -x. Right is +y.
Front-right (22.5 to 45 deg right of front): Between West and North-West.
Front-slight-right (0 to 22.5 deg right): Almost West.

Objects:
- `lego man`: First sighting (0,0) facing N -> front-left (-x, +y). Second sighting (0,0) facing W -> front-right (+y relative to W? No, right of West is North). Consistent. Let's put Lego man at (-2, 4).
- `green door`: (0,0) facing E -> front, near. Let's say (2, 0).
- `backpack`: (0,0) facing S -> front-right. Right of South is West. So South-West. (-2, -3).
- `shoppingcart`: (0,0) facing S -> front-left. Left of South is East. So South-East. (2, -3).
- `bike`: (0,0) facing W -> front-slight-right. Right of West is North. So West-North-West. (-3, 1).
- `red door`: (0,0) facing W -> front, slightly far. (-5, 0).

From Red Door (-5,0) facing West:
- `rubberduck`: front-slight-right (West-ish North). Slightly far (~5). (-9, 1).
- `truck`: front-right (North-West). Mid (~3). (-7, 2).
- `lamp`: front-right (North-West). Slightly far (~5). (-8, 4).

Agent is at red door (-5,0) facing West.

Let's verify facings of objects:
- Lego man: facing backward (first view facing N) -> faces S. facing left (second view facing W) -> faces S. Consistent.
- Backpack: facing forward (view facing S) -> faces N (opposite to agent? No, "facing forward" usually means facing the viewer? Or same direction? "facing forward" usually means facing the same way the agent is facing? No, standard convention: "facing forward" = object's front is towards agent? Or object is facing the direction of the agent's gaze?
Actually, "facing forward" in egocentric usually means the object is facing the same direction as the agent.
Wait, "facing backward" -> object's front is away from agent? Or towards?
Usually:
- facing agent (towards agent) = ?
- facing away (same direction as agent) = ?
Let's check the rules/examples if available. "facing backward" (ego) usually means the object is facing away from the agent (180 deg diff). "facing forward" usually means facing the agent. Or vice versa.
Let's assume standard NLP orientation:
- Agent facing North. Lego man "facing backward". If "facing backward" means facing South (towards agent's origin), or facing North (away)?
- Let's look at relations: "bike is west... facing left". Agent facing W. Left is S. So bike faces S.
- Lego man facing N (agent) -> "facing backward"? No.
- Let's assume absolute facings are best guess or omitted if unsure, but prompt asks for "facing".
- Let's look at Lego man:
View 1 (facing N): "facing backward". If agent faces N, backward is S.
View 2 (facing W): "facing left". If agent faces W, left is S.
So Lego man faces South.
- Backpack (facing S): "facing forward". If agent faces S, forward is S. So Backpack faces South? Or does it mean facing North (towards agent)?
Usually "facing you" is distinct. "Facing forward" often implies the object's intrinsic front is aligned with the agent's view direction. Let's assume Backpack faces South.
- Shoppingcart (facing S): "facing right". Right of S is W. Shoppingcart faces West.
- Bike (facing W): "facing left". Left of W is S. Bike faces South.
- Truck (facing W): "facing backward". Backward of W is E. Truck faces East.
- Rubberduck (facing W): "facing right". Right of W is N. Rubberduck faces North.

Map construction:
Agent: pos [-5, 0], facing "west".
Objects:
- lego man: [-2, 4], facing "south"
- green door: [2, 0]
- backpack: [-2, -3], facing "south"
- shoppingcart: [2, -3], facing "west"
- bike: [-3, 1], facing "south"
- red door: [-5, 0]
- rubberduck: [-9, 1], facing "north"
- truck: [-7, 2], facing "east"
- lamp: [-8, 4]

Wait, green door was "near" (dist 0-2). Red door was "slightly far" (dist 4-8).
Let's approximate positions on integer grid.
Lego man: "front-left, slightly far". Dist ~5. Angle ~30 deg left. x = -2.5, y = 4.3. Round to [-2, 4] or [-3, 4].
Bike: "mid distance" (2-4). x ~ -3, y ~ 1.
Red door: "slightly far" (4-8). x ~ -5 or -6. Let's use [-5, 0].

Looks consistent.

FINAL ANSWER:
```json
{
"agent": {"position": [-5, 0], "facing": "west"},
"lego man": {"position": [-2, 4], "facing": "south"},
"green door": {"position": [2, 0]},
"backpack": {"position": [-2, -3], "facing": "south"},
"shoppingcart": {"position": [2, -3], "facing": "west"},
"bike": {"position": [-3, 1], "facing": "south"},
"red door": {"position": [-5, 0]},
"rubberduck": {"position": [-9, 1], "facing": "north"},
"truck": {"position": [-7, 2], "facing": "east"},
"lamp": {"position": [-8, 4]}
}
```

THINK:
I need to construct the JSON map based on my observations.
Initial State: Agent at (0,0), facing North.

1. **Step 1 (Face North):**
* Observed: `lego man` (front-left, slightly far). "Slightly far" is (4,8]. Let's estimate distance ~5 or 6. Front-left is approx -45 to -22.5 deg. In (x...

{
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "west"
  },
  "lego man": {
    "position": [
      -2,
      4
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "rubberduck": {
    "position": [
      -9,
      1
    ],
    "facing": "north"
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -8,
      4
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "west"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "west"
  }
}

THINK:
I am at the red door. I was facing West before jumping, and JumpTo does not change orientation, so I am still facing West (global). The red door connects Room 1 (East of door) and a new room (West of door).
My observation from the red door (facing West) reveals:
- rubberduck: front-slight-right, slightly far, facing right.
- truck: front-right, mid distance, facing backward.
- lamp: front-right, slightly far. (No facing reported for lamp? Instructions say "Include only observed objects... include facing key if the object has facing direction". The prompt says "lamp: ... facing: none reported". Wait, the prompt just said "lamp: front-right, slightly far." I will omit facing for lamp.)

Distance bins:
- near: (0, 2]
- mid distance: (2, 4]
- slightly far: (4, 8]

Mapping local coordinates (Agent at origin (0,0), facing +y in local frame):
Current global facing is West. So Local +y is Global West.
Local +x is Global North (Right of West).
Local -x is Global South (Left of West).

Objects:
1. **rubberduck**:
- Bearing: front-slight-right. "front-slight-right" is bin (0°, 22.5°]. Let's estimate angle ~15°.
- Distance: slightly far. (4, 8]. Let's estimate ~6.
- Local Position: x = d*sin(theta), y = d*cos(theta).
- x ≈ 6 * sin(15°) ≈ 6 * 0.26 ≈ 1.5
- y ≈ 6 * cos(15°) ≈ 6 * 0.96 ≈ 5.8
- Let's approximate to integers/grid: Maybe (2, 6)?
- Facing: "facing right". "Right" relative to *me* or *object*? Usually reports egocentric "facing right" means the object's front is to my right.
- Wait, the instruction says "Relationship: ... Orientation: ... -forward/backward/right/left (ego)". And the prompt output says "facing right". This implies the object is facing towards the agent's right.
- Agent is facing Local +y. Agent's right is Local +x. So object is facing Local +x.
- Wait, standard convention in these prompts:
- "facing right" means the object's intrinsic front is pointing to the agent's right.
- Agent's right is local +x. So object facing is "+x".

2. **truck**:
- Bearing: front-right. Bin (22.5°, 45°]. Let's estimate ~35°.
- Distance: mid distance. (2, 4]. Let's estimate ~3.5.
- Local Position:
- x ≈ 3.5 * sin(35°) ≈ 3.5 * 0.57 ≈ 2
- y ≈ 3.5 * cos(35°) ≈ 3.5 * 0.82 ≈ 2.9 -> 3
- Approx (2, 3).
- Facing: "facing backward". Backward relative to agent. Agent faces +y. Backward is -y. So object facing "-y".

3. **lamp**:
- Bearing: front-right. Bin (22.5°, 45°]. Let's estimate ~35°.
- Distance: slightly far. (4, 8]. Let's estimate ~6 (same bin as rubberduck, maybe further than truck).
- Local Position:
- x ≈ 6 * sin(35°) ≈ 3.4
- y ≈ 6 * cos(35°) ≈ 4.9
- Approx (3, 5).
- Facing: Not specified.

Wait, I need to check the exact wording for "facing".
Instructions: "Orientation: -forward/backward/right/left (ego)... When agent faces north: forward = north, right = east..."
Observation: "rubberduck... facing right".
So relative to agent (facing local +y), the duck faces local +x.
Observation: "truck... facing backward".
Relative to agent (facing local +y), the truck faces local -y.

Let's refine coordinates.
Rubberduck: front-slight-right (0-22.5), slightly far (4-8). Say (1, 6).
Truck: front-right (22.5-45), mid (2-4). Say (2, 3).
Lamp: front-right (22.5-45), slightly far (4-8). Say (4, 5).

The prompt asks for a "Local Cognitive Map" JSON.
"origin": "agent"
"objects": { ... }
Positions relative to agent's current frame (+y is agent's front).

Let's finalize the JSON.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"rubberduck": {"position": [2, 6], "facing": "+x"},
"truck": {"position": [2, 3], "facing": "-y"},
"lamp": {"position": [4, 5]}
}
}
```

THINK:
I am at the red door. I was facing West before jumping, and JumpTo does not change orientation, so I am still facing West (global). The red door connects Room 1 (East of door) and a new room (West of door).
My observation from the red door (facing West) reveals:
- rubberduck: front-slight-rig...

{
  "origin": "agent",
  "objects": {
    "rubberduck": {
      "position": [
        2,
        6
      ],
      "facing": "+x"
    },
    "truck": {
      "position": [
        2,
        3
      ],
      "facing": "-y"
    },
    "lamp": {
      "position": [
        4,
        5
      ]
    }
  }
}

{
  "truck": {
    "position": [
      1,
      2
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      5,
      6
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      1,
      6
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "rubberduck": {
      "position": [
        2,
        6
      ],
      "facing": "+x"
    },
    "truck": {
      "position": [
        2,
        3
      ],
      "facing": "-y"
    },
    "lamp": {
      "position": [
        4,
        5
      ]
    }
  }
}

{
  "truck": {
    "position": [
      1,
      2
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      5,
      6
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      1,
      6
    ],
    "facing": "north"
  }
}

THINK:
I am at the red door (West wall of Room 1). My previous position was (0,0) in Room 1.
I scanned Room 1.
- North of (0,0): Lego man.
- East of (0,0): Green door.
- South of (0,0): Backpack, Shopping cart.
- West of (0,0): Red door, Bike, Lego man.

I jumped to the red door. Since I was facing West and the door was "front, slightly far", the door is roughly at (-X, 0) relative to origin, or maybe (-X, Y). The map shows my position '*' on a wall between two rooms. The room to the right (East) is Room 1 (where I came from). The room to the left (West) is the new room.
My current orientation is West.
I observe:
- Rubberduck: front-slight-right (West-North-West ish)
- Truck: front-right (North-West ish)
- Lamp: front-right (North-West ish)

Looking at the map provided:
The agent '*' is on a vertical wall.
To the right is the explored room (Room 1).
To the left is the unexplored room.
The points A, B, C, D, E, F are in the left room.
Since I am looking West (into the left room) and have observed some objects (rubberduck, truck, lamp) which appear to be front-right (North-West), the area immediately West and North-West of me is partially observed.
However, I need to identify which specific candidate points (A-Z) are in *unexplored* regions.
The FOV is 90 degrees. Facing West, I see West +/- 45 degrees. So I see West-North-West to West-South-West.
The objects seen are:
- Rubberduck: front-slight-right -> West + a bit North.
- Truck: front-right -> West + 45 deg North (North-West).
- Lamp: front-right -> North-West.

So I see the cone pointing West.
Point A: West of me, slightly South. Probably in FOV (front-slight-left or front).
Point B: West and slightly North. Probably in FOV.
Point D: Far West.
Point C: North-West.
Point E: Far North-West.
Point F: North, close to the wall.

Let's look at the map grid more closely.
Agent '*' is at the door.
Points A, B, D are directly West-ish.
Points C, F are North-West-ish.
Point E is far North-West.

Wait, the "Fog Probe" asks to select points in *unexplored/unobserved* regions.
I just observed from the red door facing West.
I saw objects "front-slight-right" (West-North) and "front-right" (North-West).
My FOV covers [-45, 45] relative to West. That is [SW, NW].
So I see the region to the West.
A is directly West/South-West. Likely visible.
B is West/North-West. Likely visible.
D is far West. The distance bins go up to "extremely far". "Slightly far" was used for objects. D looks "far". Might be visible or on the edge.
C and F are North-West.
F is very close to the wall North of the door. "Front-right" covers North-West.
E is far North.
Let's consider the room shape.
The prompt says "Select the points that are located in unexplored/unobserved regions."
I haven't rotated to look South or North inside this new room yet. I only looked West (Front).
So regions to the "Right" (North) and "Left" (South) outside the +/- 45 degree cone are unobserved?
Actually, "front-right" goes up to 45 degrees.
If I am facing West:
Front = West.
Front-Right = North-West.
Front-Left = South-West.
So I see a cone pointing West.
I do *not* see directly North or South (behind the wall plane, or > 45 degrees).
Looking at the map:
F is North-East relative to the room center, but relative to the door (where I am), it's North.
The door is on the wall.
Coordinates:
If * is at (x,y), A is (x-2, y), B is (x-2, y+2), etc.
Facing West.
Visible: West cone.
F is at (x, y+2). Angle is 90 deg (Right). This is "Right", not "Front-Right". Front-Right is (22.5, 45]. Right is > 45.
So F is likely unobserved.
C is at (x-2, y+3). Angle is atan(2/3) relative to x-axis... no, relative to West. dx=-2, dy=3. Angle from West (180) is... vector (-2, 3). Angle is roughly 123 degrees. Difference from West (180) is 57 degrees. Outside 45. So C is unobserved.
E is at (x-4, y+6). Vector (-4, 6). Angle similar to C. Unobserved.
A is at (x-2, y). Vector (-2, 0). Angle 0 relative to West. Observed.
B is at (x-2, y+2). Vector (-2, 2). Angle 45 degrees relative to West. Boundary. Might be observed? Usually FOV is strict. "Front-right" is up to 45. If it's exactly 45, it's visible. If >45, not.
D is at (x-6, y+2). Vector (-6, 2). Angle small. Observed.

Wait, let's re-evaluate "unobserved".
I have only looked West.
Points definitely unseen:
- F (straight Up/North along the wall) - Angle 90 deg relative to facing.
- C (North-West, steep angle) - Vector (-2, 3). Angle > 45.
- E (North-West, steep angle) - Vector (-4, 6) ~ (-2, 3). Angle > 45.
Points likely seen:
- A (West).
- B (West-North-West). Vector (-2, 2) is 45 deg.
- D (West).

Let's refine B. (-2, 2) is exactly 45 degrees. Is 45 included?
"Cardinal angle bins... (292.5, 337.5] -> north west".
"Egocentric... (22.5, 45] -> front-right".
It seems 45 is included in front-right. So B is observed.
C is (-2, 3). atan(1.5) = 56 deg. > 45. Unobserved.
E is (-4, 6). atan(1.5) = 56 deg. > 45. Unobserved.
F is (0, 2). 90 deg. Unobserved.

So unobserved: C, E, F.
What about the room to the right (Room 1)?
I explored Room 1 thoroughly (360 scan). The map shows the area to the right of '*' is empty of letters, implying it's not the target of the probe or already known. The letters are in the left room.

So I will select C, E, F.
Wait, let's check A. A is at (-2, 0). Visible.
Let's check D. D is at (-6, 2) or so. Visible.
Let's check B. B is (-2, 2). Visible.

Is there any blockage?
The objects I saw: rubberduck (front-slight-right), truck (front-right), lamp (front-right).
Rubberduck is likely near B?
Truck/Lamp near C? If I saw them, C might be observed?
Wait, if I saw an object at C, then C is observed.
I saw "truck: front-right" and "lamp: front-right".
Front-right is (22.5, 45].
If C is at angle 56, it would be "right" or "beyond-fov" if FOV is 90 (+/- 45).
If I saw objects, they must be within +/- 45.
The objects I saw were "front-right".
Does that mean C is actually within 45?
Coordinates on map are symbolic.
Let's assume the map grid is accurate to the layout.
Grid counts:
Start at * (say x=0, y=0).
A: x=-3, y=0.
B: x=-3, y=2.
D: x=-7, y=2.
F: x=0, y=3.
C: x=-3, y=4.
E: x=-5, y=7.

Let's check angles again with these counts.
Facing West (-1, 0).
A (-3, 0): Angle 0. Visible.
B (-3, 2): atan(2/3) = 33.7 degrees. < 45. Visible.
D (-7, 2): atan(2/7) = 16 degrees. Visible.
F (0, 3): 90 degrees. Not visible.
C (-3, 4): atan(4/3) = 53 degrees. > 45. Not visible.
E (-5, 7): atan(7/5) = 54 degrees. > 45. Not visible.

So C, E, F are outside the West-facing FOV.
Therefore, they are unobserved.

One detail: "Observe() ... reports objects ... in your FOV".
The prompt asks for points in "unexplored/unobserved regions".
Since I haven't looked North or South in this room, the regions > 45 degrees are unobserved.
So C, E, F are the answer.

Double check F. F is along the wall I am standing on?
Map:
#....CF#
#......#
#D..B..#
#..A...*
The wall is at x=0. * is at (0,0).
F is at (-1, 4)? No, F is next to C.
Let's trace lines.
Row of *: #..A...*
Row above: #D..B..#
Row above: #......#
Row above: #....CF#
Wait, F is in the same column as B? No.
Let's count columns from *.
Col 0: *
Col -1: .
Col -2: .
Col -3: .
Col -4: A (appears to be in col -4 from *)
Actually let's count '.'
Row *: # . . A . . . * (3 dots between A and *) -> A is at x=-4 relative to *.
Row +1 (D, B): # D . . B . . #
B is above A? Visually B looks shifted right of A.
Let's align the columns carefully.
#....CF#......
#......#......
#D..B..#......
#..A...*......
Columns:
12345678 (indices in string segment)
Row A: # (1) . (2) . (3) A (4) . (5) . (6) . (7) * (8)
So A is at column 4. * is at column 8. dx = -4.
Row B: # (1) D (2) . (3) . (4) B (5) . (6) . (7) # (8)
So B is at column 5. dx = -3.
Row C/F: # (1) . (2) . (3) . (4) . (5) C (6) F (7) # (8)
So C is at col 6 (dx = -2). F is at col 7 (dx = -1).
Row spacing:
Row A is y=0.
Row B is y=2? (There is a row of dots between them? No, looking at the snippet:
#D..B..#
#..A...*
There is NO empty row between them in the text block provided?
Wait, the example map has:
#D..B..#
#..A...*
They are adjacent rows?
Let's check the full map provided.
#......#......########
#D..B..#......#......#
#..A...*......+......#
Yes, Row with A is below Row with B.
Let's count Y.
Row *: y=0.
Row B: y=1.
Row empty: y=2.
Row CF: y=3.
Row E: y=5 (gap of 1 row).

Re-evaluating coordinates with this grid:
* is at (0,0). Orientation West.
A: (-4, 0). Angle 0. Visible.
B: (-3, 1). atan(1/3) = 18 deg. Visible.
D: (-6?, 1). D is at col 2. * at col 8. dx = -6. atan(1/6) = 9 deg. Visible.
C: (-2, 3). atan(3/2) = 56 deg. > 45. Not visible.
F: (-1, 3). atan(3/1) = 71 deg. > 45. Not visible.
E: Top row.
Row CF is y=3.
Row above: y=4.
Row E: y=5.
E is at col 4 (aligned with A?).
#..E...
#......
#....CF
Col E is roughly col 4. dx = -4.
Pos E: (-4, 5). atan(5/4) = 51 deg. > 45. Not visible.

So C, E, F are definitely not visible in a single West-facing cone.
Result: C, E, F.

Are there any others?
The list of candidates is A, B, C, D, E, F.
A, B, D are visible.
C, E, F are not.

Final check.
Is it possible "front-right" covers up to 60 degrees or something?
"Egocentric angle bins ... (22.5, 45] -> front-right".
No, strictly up to 45.
Beyond 45 is "beyond-fov" (which typically implies not seen, or reported as such if the agent can see 360 but bins it. But the rules say "FOV is 90 ... can NOT see objects outside your FOV").
So I cannot see C, E, F.

Result: C, E, F.

Wait, looking at the map again.
Row * and Row B are adjacent.
Row B and Row CF have ONE empty row between them.
Row CF and Row E have ONE empty row between them.
Coordinates:
A: (-4, 0)
B: (-3, 1)
D: (-6, 1)
C: (-2, 3)
F: (-1, 3)
E: (-4, 5)

Calculated Angles from West (axis -x):
A: 0 deg.
B: atan(1/3) = 18.4 deg.
D: atan(1/6) = 9.5 deg.
C: atan(3/2) = 56.3 deg.
F: atan(3/1) = 71.6 deg.
E: atan(5/4) = 51.3 deg.

FOV is +/- 45 deg.
Visible: A, B, D.
Not visible: C, F, E.

The logic holds.

One small nuance: "When located in a doorway ... you can see into both connected rooms".
Does this imply a wider FOV? No, "within FOV" is specified.
The benefit is seeing *across* the boundary, not widening the angle.
So strict 90 degree cone applies.

Final Answer seems to be C, E, F.

Is D "explored"? I see it. It's in the "unexplored room", but the *region* D is in is now observed. The question asks for points located in unexplored/unobserved regions. Since I have observed the region containing D, D is not in an unobserved region. C, E, F are in regions I haven't seen (dark).

One sanity check on "Candidate points".
Usually "A", "B"... denote specific cells.
If I see the cell, it's observed.
If I don't, it's unobserved.
So C, E, F.

JSON format required.

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

THINK:
I am at the red door (West wall of Room 1). My previous position was (0,0) in Room 1.
I scanned Room 1.
- North of (0,0): Lego man.
- East of (0,0): Green door.
- South of (0,0): Backpack, Shopping cart.
- West of (0,0): Red door, Bike, Lego man.

I jumped to the red door. Since I was facing ...

######################
#..E...###############
#......###############
#....CF#......########
#......#......########
#D..B..#......#......#
#..A...*......+......#
########......#......#
########......#......#
###############......#
###############......#
######################

You jumped to red door. You observe:
• rubberduck: front-slight-right, slightly far, facing right
• truck: front-right, mid distance, facing backward
• lamp: front-right, slightly far.
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 red door. You observe:
• rubberduck: front-slight-right, slightly far, facing right
• truck: front-right, mid distance, facing backward
• lamp: front-right, slightly far.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step a...

I am at the red door, facing West.
Observations into the new room (let's call it Room 2):
- Rubberduck (front-slight-right)
- Truck (front-right)
- Lamp (front-right)

The view covers the West/North-West sector relative to the door. I need to map this new room fully. Since I am at the doorway, I have a good vantage point but my FOV is limited. I should step into the room to get a better view or rotate to see more from the door. Jumping to an object inside the room would establish a presence there.
However, I haven't seen the whole room. I am facing West.
I should scan the rest of Room 2. Rotating while at the door might reveal more, or I can jump to an object like the truck to be inside the room. Jumping to the truck seems efficient to change my vantage point.
Wait, if I jump to the truck, I will be inside Room 2. The truck is "mid distance" to the front-right.
Let's first rotate to see the other side of the room from the door to ensure I don't miss corners near the door. If I rotate 90 degrees clockwise (to North), I might see what's "above" the door. If I rotate 90 degrees counter-clockwise (to South), I see "below".
Actually, the objects seen (duck, truck, lamp) are generally in front.
Let's jump to the truck to get fully inside Room 2 and observe from there. The truck is at a mid distance.

I am at the red door, facing West.
Observations into the new room (let's call it Room 2):
- Rubberduck (front-slight-right)
- Truck (front-right)
- Lamp (front-right)

The view covers the West/North-West sector relative to the door. I need to map this new room fully. Since I am at the doorway, I hav...

THINK:
I need to update the cognitive map based on the observations.
My initial position is (0,0), facing North.

**Step 1: Initial Scan (0,0)**
1. **Face North**: Observed `lego man` (front-left, slightly far).
* Agent (0,0) facing N.
* Lego man is front-left (NW). "Slightly far" is (4,8]. Let's estimate distance ~5-6. Angle ~ -30 to -45. Position approx (-3, 4). Facing: backward (South).
2. **Face East**: Observed `green door` (front, near, on front wall).
* Agent (0,0) facing E.
* Green door is front (East). "Near" is (0,2]. Let's say (2, 0).
3. **Face South**: Observed `backpack` (front-right) and `shoppingcart` (front-left).
* Agent (0,0) facing S.
* Backpack: Front-Right relative to South is South-West. "Mid distance" (2,4]. Approx (-2, -2). Facing: forward (relative to agent? No, "facing forward" usually means facing the agent or North? The instruction says "facing: forward/backward... (ego)". If object faces forward, it faces same direction as agent? Or faces the agent? Usually in these tasks "facing forward" means facing the viewer or facing the same way. Let's assume standard ego: faces same direction as agent (South). Wait, standard usually means "facing away". Let's assume absolute orientation. "facing forward" relative to agent facing South. If agent faces South, forward is South. So backpack faces South. Let's stick to the labels provided.
* Shoppingcart: Front-Left relative to South is South-East. "Mid distance". Approx (2, -2). Facing: right (West, relative to agent facing South? Right of South is West).
* Relation: Backpack is East, near to Shoppingcart?
* Wait, the text says: "Assume your current facing direction is called 'north': backpack is east, near to shoppingcart."
* Current facing is South (real). So "North" (relative) = South (real).
* "East" relative to "North"(South) is West (real).
* So Backpack is West of Shoppingcart. This matches my coordinate estimation: Backpack (-2,-2), Cart (2,-2).
4. **Face West**: Observed `bike`, `lego man`, `red door`.
* Agent (0,0) facing W.
* Red door: Front (West). "Slightly far" (4,8]. Let's say (-5, 0).
* Lego man: Front-Right relative to West is North-West. Seen before.
* Bike: Front-slight-right. "Mid distance". Approx (-4, 1). Facing: left (South, relative to agent facing West? Left of West is South).
* Relation: Bike is West of Lego man? (Relative "North"=West). "East" relative to West is North. "West" relative to West is South. So Bike is South of Lego man. Lego man (-3, 4), Bike (-4, 1). This is roughly consistent.

**Step 2: Move to Red Door**
* Jumped to `red door`. Estimated pos (-5, 0). Orientation: West.
* Observe: `rubberduck`, `truck`, `lamp`.
* Rubberduck: Front-slight-right (W-NW). Slightly far. Approx (-10, 2). Facing: right (North, relative to West facing? Right of West is North).
* Truck: Front-right (NW). Mid distance. Approx (-7, 2). Facing: backward (East, relative to West facing? Backward of West is East).
* Lamp: Front-right (NW). Slightly far. Approx (-8, 4).

**Step 3: Move to Truck**
* Jumped to `truck`. Estimated pos (-7, 2). Orientation: West (JumpTo doesn't change orientation).
* Observe: `rubberduck`, `lamp`.
* Rubberduck: Front (West). Mid distance. Let's say (-10, 2). Facing: right.
* Lamp: Front-right (NW). Slightly far.

**Consolidating Coordinates:**
* **Agent**: Now at `truck`. Pos ~(-7, 2). Facing West.
* **Lego man**: ~(-3, 4). Facing South.
* **Green door**: ~(2, 0).
* **Backpack**: ~(-1, -2). Facing South (assuming 'forward' means agent's direction). Or if 'facing forward' means facing the agent, it would be North. Let's assume absolute 'facing' isn't derived yet, just relative. But I need to output `facing` in the JSON. The prompt says "facing: forward/backward/right/left (ego)". "facing forward" usually means facing the same direction as the agent. Agent was facing South. So Backpack faces South.
* **Shoppingcart**: ~(2, -2). Agent facing South. "Facing right". Right of South is West. Cart faces West.
* **Bike**: ~(-3, 1). Agent facing West. "Facing left". Left of West is South. Bike faces South.
* **Red door**: ~(-5, 0).
* **Truck**: ~(-7, 2). Agent facing West. "Facing backward". Backward of West is East. Truck faces East.
* **Rubberduck**: ~(-10, 2). Agent facing West. "Facing right". Right of West is North. Duck faces North.
* **Lamp**: ~(-9, 5).

Let's refine coordinates based on "Near" (0-2), "Mid" (2-4), "Slightly far" (4-8).
* (0,0) -> Red Door (West, slightly far): (-5, 0) is good.
* (0,0) -> Green Door (East, near): (2, 0) is good.
* (0,0) -> Lego Man (NW, slightly far): (-3, 4). Dist 5. Good.
* (0,0) -> Backpack (SW, mid): (-2, -2). Dist 2.8. Good.
* (0,0) -> Shopping Cart (SE, mid): (2, -2). Dist 2.8. Good.
* (0,0) -> Bike (W-NW, mid): (-3, 1). Dist 3.1. Good.

At Red Door (-5, 0) facing West:
* Truck (Front-right, mid): (-5,0) + (dx, dy). Front is -x. Right is +y. Front-Right is (-x, +y). Mid (2-4). Let's say (-2, 2) relative. Abs: (-7, 2).
* Rubberduck (Front-slight-right, slightly far): Angle small. Dist 4-8. (-5,0) + (-5, 1). Abs: (-10, 1).
* Lamp (Front-right, slightly far): (-5,0) + (-4, 4). Abs: (-9, 4).

At Truck (-7, 2) facing West:
* Rubberduck (Front, mid): (-7, 2) + (-3, 0). Abs: (-10, 2). Consistent.
* Lamp (Front-right, slightly far): (-7, 2) + (-3, 3). Abs: (-10, 5). Consistent-ish.

JSON Map Construction:
Agent: (-7, 2), West.
Lego man: (-3, 4), South.
Green door: (2, 0).
Backpack: (-2, -2), South.
Shoppingcart: (2, -2), West.
Bike: (-3, 1), South.
Red door: (-5, 0).
Truck: (-7, 2), East.
Rubberduck: (-10, 2), North.
Lamp: (-9, 5).

Wait, I need to check the "facing" interpretations again.
Observation 1 (N): Lego man facing backward. Agent N. Backward is S.
Observation 3 (S): Backpack facing forward. Agent S. Forward is S. Shoppingcart facing right. Agent S. Right is W.
Observation 4 (W): Bike facing left. Agent W. Left is S. Lego man facing left. Agent W. Left is S. (Consistent).
Observation 5 (Door W): Truck facing backward. Agent W. Backward is E. Rubberduck facing right. Agent W. Right is N.
Observation 6 (Truck W): Rubberduck facing right. Agent W. Right is N. (Consistent).

FINAL ANSWER:
```json
{
"agent": {"position": [-7, 2], "facing": "west"},
"lego man": {"position": [-3, 4], "facing": "south"},
"green door": {"position": [2, 0]},
"backpack": {"position": [-2, -2], "facing": "south"},
"shoppingcart": {"position": [2, -2], "facing": "west"},
"bike": {"position": [-3, 1], "facing": "south"},
"red door": {"position": [-5, 0]},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-10, 2], "facing": "north"},
"lamp": {"position": [-9, 5]}
}
```

THINK:
I need to update the cognitive map based on the observations.
My initial position is (0,0), facing North.

**Step 1: Initial Scan (0,0)**
1. **Face North**: Observed `lego man` (front-left, slightly far).
* Agent (0,0) facing N.
* Lego man is front-left (NW). "Slightly far" is (4...

{
  "agent": {
    "position": [
      -7,
      2
    ],
    "facing": "west"
  },
  "lego man": {
    "position": [
      -3,
      4
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "backpack": {
    "position": [
      -2,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -2
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -10,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -9,
      5
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "west"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "west"
  }
}

THINK:
I am at the truck's position. I previously faced West at the red door. I jumped to the truck which was front-right (relative to West facing).
My orientation hasn't changed, so I am still facing West (Allo West).
In the local frame (Agent facing +y):
- West is +y.
- North is +x.
- South is -x.
- East is -y.

From the truck, I observe:
- rubberduck: front (local +y), mid distance.
- lamp: front-right (local +x, +y quadrant), slightly far.

Wait, I need to generate the local map based on the *current* observation `Observe()` which lists:
- rubberduck: front, mid distance
- lamp: front-right, slightly far

Distance bins:
- mid distance: (2, 4]. Let's estimate 3.
- slightly far: (4, 8]. Let's estimate 6.

Mapping to local coordinates (Agent is at (0,0), facing +y):
- rubberduck: "front" means ~0 degrees. Distance ~3. Position ~[0, 3]. Facing: previous observation said "facing right". Right relative to whom? The previous observation was from the door (facing West). Duck was facing right (North). If Duck faces North, and Agent faces West (local +y), then North is local +x. So Duck facing is +x. The current observation says "facing right" is not mentioned in the text provided in the prompt "You observe: • rubberduck: front, mid distance, facing right". Ah, it *is* there. "facing right". So relative to agent's current frame (+y), right is +x. So Duck faces +x.
- lamp: "front-right" means ~45 degrees. Distance ~6. Position ~[4, 4]. Facing: previous obs didn't specify, current obs doesn't specify.

Wait, I need to be careful with coordinate conversion.
Observation:
"rubberduck: front, mid distance, facing right" -> Position: [0, 3], Facing: "+x"
"lamp: front-right, slightly far" -> Position: [4, 4] (approx), No facing.

Let's refine coordinates.
Front-right is 22.5 to 45 degrees. 45 deg at dist 6: x=4.2, y=4.2. Integer approx [4, 4].
Front is 0 degrees. Dist 3: x=0, y=3.

Wait, looking back at the prompt's output for `JumpTo(truck)`:
`• rubberduck: front, mid distance, facing right`
`• lamp: front-right, slightly far.`

So I construct the JSON.

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"rubberduck": {"position": [0, 3], "facing": "+x"},
"lamp": {"position": [4, 4]}
}
}

THINK:
I am at the truck's position. I previously faced West at the red door. I jumped to the truck which was front-right (relative to West facing).
My orientation hasn't changed, so I am still facing West (Allo West).
In the local frame (Agent facing +y):
- West is +y.
- North is +x.
- South is -x....

{
  "origin": "agent",
  "objects": {
    "rubberduck": {
      "position": [
        0,
        3
      ],
      "facing": "+x"
    },
    "lamp": {
      "position": [
        4,
        4
      ]
    }
  }
}

{
  "lamp": {
    "position": [
      4,
      4
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      0,
      4
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "rubberduck": {
      "position": [
        0,
        3
      ],
      "facing": "+x"
    },
    "lamp": {
      "position": [
        4,
        4
      ]
    }
  }
}

THINK:
I am currently at the 'truck' in Room 2 (West room).
Initial position was (0,0) in Room 1 (Center).
Room 1 is connected to Room 2 (West) via the red door.
I moved West to the red door, then jumped to the truck which was front-right (relative to West facing, so North-West) from the door.
Looking at the map:
- The agent is at `*`.
- The red door is likely the `+` to the East of the agent (connecting to the middle room).
- The map shows three rooms: Left (Room 2), Middle (Room 1), Right (Room 3?).
- I have observed the 'truck', 'rubberduck', and 'lamp' in Room 2.
- Candidate A is in the far North-West corner.
- Candidate B is in the North-West area.
- Candidate C is South-West of the agent.
- Candidate D is near the East wall of Room 2 (North of the door).
- Candidate E is West of D.
- Candidate F is near the door.
- The rightmost room is completely unexplored.
- The middle room has been scanned 360 degrees.
- I am in the left room. I looked "Front" (West) from the door and saw the truck (Front-Right relative to West -> North-West).
- From the truck (facing West), I observed the rubberduck (Front) and lamp (Front-Right).
- This means I have seen the area to the West and North-West of the truck.
- Areas "behind" me (East, South) or to the far South-West in this room might be unobserved from this specific vantage point, although I saw some from the door.
- Specifically, point C (South-West) might be unobserved if I haven't looked South. I looked West from the door (seeing front-right stuff). I haven't looked Left (South) from the door or from the truck. So C is likely unobserved.
- Points A and B are in the North/North-West. The rubberduck and lamp are in that direction. I have likely observed the space around B and E. A is very far, maybe beyond range or blocked? But "unexplored" usually means strictly not seen.
- Let's look at the labels relative to my path.
- Start Room 1 (Middle). Scanned 360.
- Jump to Red Door (between Left and Middle).
- Looked West into Left Room. Saw Truck, Duck, Lamp (all roughly NW).
- Jumped to Truck. Looked West. Saw Duck, Lamp.
- I have NOT looked South in the Left Room. So area C is definitely unexplored.
- I have NOT looked North in the Left Room explicitly, but the objects were to the right (North). However, A is in the far corner.
- In the map provided, the agent `*` is at the truck position.
- The area to the right (East) is the wall/door I came from.
- The area to the left (West) is where I am facing.
- C is "below" (South). I haven't looked South.
- The map shows the Middle Room is explored (no dots there except maybe walls?). Wait, the map shows dots `.` in the middle room too, but no letters.
- The Right Room has no letters.
- The letters A, B, C, D, E, F are all in the Left Room (Room 2).
- C is in the South part. I haven't looked South.
- A, B, E, D are in the North part. I have looked generally North-West (from door) and West (from truck). The objects were visible.
- However, "unexplored" usually implies not covered by the FOV cones.
- From Door (facing West): FOV +/- 45 deg covers West. Objects were Front-Right (NW).
- From Truck (facing West): FOV +/- 45 deg covers West. Objects were Front/Front-Right.
- The North-East corner of this room (D) might be missed? I was at the door facing West. Front-Right is NW. D is NE relative to the room center, or North relative to the door. "Front-Right" (22.5 to 45 deg) from West is North-West. The area directly North (90 deg to right) is "Right", which is outside the "Front" FOV bins usually? The binning says (22.5, 45] is front-right. The "Right" bin is presumably (45, ...].
- Wait, the instruction says: "Otherwise -> beyond-fov". The bins listed are only for Front sectors [-45 to 45].
- Actually, the bins listed are: `[-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.`
- So I only see +/- 45 degrees.
- From Door (Facing West): I see West +/- 45. (NW to SW).
- I saw Truck (Front-Right -> NW).
- I did NOT see straight North or straight South.
- So D (North/East part of room near wall) is likely unseen.
- C (South part) is likely unseen.
- From Truck (Facing West): I see West +/- 45.
- I see Duck, Lamp.
- A is far West/North. Might be seen.
- B is West/North. Might be seen.
- E is near the middle.
- F is near the door.
- Since I only see a 90 degree cone, and I have only faced West, I have missed the North and South parts of the room.
- So D (North East-ish), C (South), and maybe A (Far North) are candidates.
- Let's check the map coordinates visually.
- Agent `*` is roughly (row 6, col 6).
- Door `+` is at (row 6, col 10).
- C is at (row 6, col 3). Wait, row 6? No, C looks lower.
- Row indices usually start from bottom.
- Let's trace the map string.
- Row 0 (bottom): #...#
- Row 1: #...#
- Row 2: #...#
- Row 3: #......+......+......#
- Row 4: #..C.*.#......#......#
- Row 5: #.....F#......########
- Row 6: #..E..D#......########
- Row 7: #..B...###############
- Row 8: #....A.###############
- Row 9: ######################
- Agent `*` is in Row 4.
- C is in Row 4, to the left of Agent. Facing West?
- If I am at `*` facing West, C is directly in front!
- Wait, the map might not be aligned with my facing.
- The map legend says "North is Up".
- I am facing West. West is "Left" on the map.
- So from `*`, looking Left (West), I see C?
- Wait, let's re-read the observation from the Truck.
- "rubberduck: front, mid distance... lamp: front-right..."
- If I am at `*` facing West (Left), "Front" is Left.
- So C is likely observed if it is in the cone.
- The map shows C is to the Left of `*`. So C is in front.
- D is "Up" and "Right" (North-East relative to map, Back-Right relative to agent). Unseen.
- E is "Up" and "Left" (North-West relative to map, Front-Right relative to agent). Seen (Lamp/Duck area).
- F is "Right" (East, Back relative to agent). Unseen.
- A, B are "Up" (North, Right relative to agent). Unseen?
- Wait.
- Facing West (Left).
- FOV is +/- 45 deg.
- I see North-West to South-West.
- North is Right. South is Left. West is Front.
- So I see "Left-Map" +/- 45 deg.
- Candidates:
- C: West (Left on map). Seen.
- E: North-West (Up-Left on map). Seen.
- B: North-West (Up-Left on map). Seen.
- A: North (Up on map). This is 90 deg to the right of West. This is "Right" side of agent. Unseen.
- D: North-East (Up-Right on map). Behind/Right. Unseen.
- F: East (Right on map). Behind. Unseen.
- Wait, looking at the previous observation from the Door (Facing West):
- Saw Truck (Front-Right -> North-West).
- Saw Rubberduck (Front-Slight-Right -> West-North-West).
- Saw Lamp (Front-Right -> North-West).
- From Door `+`, facing West:
- West is Front.
- North is Right.
- I saw stuff in the Front-Right quadrant (North-West).
- Did I see South-West (C)? Nothing reported in Front-Left.
- From Truck `*`, facing West:
- Saw Rubberduck (Front -> West).
- Saw Lamp (Front-Right -> North-West).
- Nothing reported Front-Left (South-West).
- C is located West/South-West on the map?
- Map layout:
Row 4: `...C.*.`
Row 3: `......+.`
Wait, let's look at the ASCII carefully.
Row with `*`: `#..C.*.#`
C is to the left of `*`.
If `*` is (x,y), C is (x-2, y).
Vector from `*` to C is (-2, 0).
Facing West (-1, 0).
Angle is 0 degrees. "Front".
Why wasn't C reported? Maybe C is empty space?
Ah, A-Z are "Candidate points" (empty space to explore), not objects.
The question asks: "Select the points that are located in unexplored/unobserved regions."
An unobserved region is one not covered by any FOV cone so far.

Path history:
1. (0,0) in Room 1. Obs North (Front). Obs East (Front). Obs South (Front). Obs West (Front).
Room 1 (middle room) is fully observed 360.
Points in middle room: None labeled.
2. Jump to Red Door (Left side of Room 1). Pos: `+` at (Row 3, Col ~6? No, looking at map).
Let's align map to rooms.
Middle block is `......#......#`.
Left block is Room 2.
Door `+` connects them.
Agent `*` is now in Left Room.
Previous loc: Door `+`.
Facing West.
FOV: West cone.
Covered: West of Door.
Specifically: (North-West sector seen due to objects). (West sector seen).
Did I see South-West from Door? No objects reported.
Did I see South from Door? No.
So South part of Room 2 is unobserved?
3. Jump to Truck `*`.
Facing West.
FOV: West cone.
Covered: West of Truck.

Let's check points A-F relative to coverage.
- F: East of Truck (Between Truck and Door). Behind agent now. From Door (facing West), F was "in front" (West of door). Distance from Door to Truck? Truck is "Mid distance" (2-4m). F is in between?
The map shows F is close to the door.
When at Door facing West, F was in FOV (Front). So F is observed.
- C: West of Truck. "Front" of agent now. Agent facing West.
C is in the FOV of the current Observe() action?
Wait, "unexplored" means "not yet observed".
I just executed `Observe()` at `*` facing West.
So the cone West of `*` is NOW observed.
C is in that cone. So C is observed.
- E: North-West of Truck. Front-Right.
Agent sees Front-Right (Lamp is there).
So E is observed.
- B: Further North-West.
Likely observed (in the cone).
- A: Far North.
From Truck (facing West), North is 90 deg Right. Outside FOV (max 45).
From Door (facing West), North is 90 deg Right. Outside FOV.
So A is Unobserved.
- D: North-East of Truck.
From Truck (facing West), D is Behind-Right. Unobserved.
From Door (facing West), D is North (Right). Unobserved.
So D is Unobserved.

Let's double check C.
C is "Front" from Truck.
If the current step's Observe() counts, C is observed.
The prompt asks "Select the points that are located in unexplored/unobserved regions."
Usually, this includes the current observation?
"You jumped to truck. You observe: ..."
The observation happened.
So the area in front of the truck is observed.
C is in front.

What about "South" of the door?
The map shows the room extends South.
The Agent is at Row 4.
Row 3 is below.
The Door is at Row 3 (relative to the block).
Wait, looking at the map again:
`#..C.*.#......#......#` (Row with *)
`#......+......+......#` (Row with +)
`########......#......#`
The room seems to end just below the door?
Or maybe there is space?
Row 2: `########`...
It looks like the south wall is close.
So maybe no points there.

Let's focus on A and D.
A is near the North wall (Top).
D is near the North-East corner.
Both are "North" relative to the agent's path (West-facing).
Since I only look West (+/- 45), I miss the North sectors.

Is B unobserved?
B is North-West.
From Truck (West), B is Front-Right.
Is it within 45 degrees?
Map:
Truck `*`: roughly x=6, y=4 (relative to room).
B: roughly x=4, y=7.
Vector: (-2, +3).
Angle: atan(3/2) approx 56 degrees.
This is > 45 degrees.
So B is likely "Right" (outside Front-Right bin).
If B is > 45 deg, it is unobserved.

Let's check E.
E: x=4, y=6.
Vector: (-2, +2).
Angle: 45 degrees.
Borderline. Usually (22.5, 45] is Front-Right.
If it is exactly 45, it is observed.
If slightly more, unobserved.

Let's check C again.
C: x=3, y=4.
Vector: (-3, 0).
Angle: 0. Observed.

Let's check F.
F: x=7, y=5.
Door `+`: x=7, y=3? No, door is at + symbol.
In the string: `......+`
Agent `*` is left of the vertical wall line?
Let's trace coordinates more carefully.
Let (0,0) be bottom-left of the whole map string.
Map width: 22 chars.
Map height: 12 rows (0 to 11).
Row 11: `######################`
Row 8: `#....A.###############` -> A at x=5.
Row 7: `#..B...###############` -> B at x=3.
Row 6: `#..E..D#......########` -> E at x=3, D at x=6.
Row 5: `#.....F#......########` -> F at x=6.
Row 4: `#..C.*.#......#......#` -> C at x=3, * at x=5.
Row 3: `#......+......+......#` -> Door at x=7.

Coordinates (x, y):
Agent `*` at (5, 4).
Door `+` at (7, 3). Note: This door connects Room 1 (Right of x=7) and Room 2 (Left of x=7).
Wait, the `+` is at x=7. The wall is at x=7 in other rows?
Rows 4-6 have `#` at x=7.
So the wall is x=7.
Room 2 is x < 7.
Room 1 is x > 7.
Agent `*` at (5, 4) is in Room 2. Correct.
Door is at (7, 3)? Or is the door the `+` at x=7?
Line 3: `#......+......+......#`
The `+` is at index 7.
This fits.

Check observations:
1. From Door (7, 3). Facing West (-1, 0).
FOV Cone: West +/- 45 deg.
Line from (7,3) to (x,y). Angle relative to (-1,0).

2. From Truck `*` (5, 4). Facing West (-1, 0).
FOV Cone: West +/- 45 deg.

Check Points:
- F (6, 5):
Relative to Door (7,3): Vector (-1, +2). Angle vs West?
West is (-1, 0). Vector is (-1, 2).
Angle: atan(2/1) approx 63 deg.
This is > 45 deg. "Right".
So F was NOT seen from Door.
Relative to Truck (5,4): Vector (+1, +1).
Truck faces West. F is Behind-Right.
So F was NOT seen from Truck.
F is Unobserved.

- D (6, 6):
Relative to Door (7,3): Vector (-1, +3). Angle > 45. Unobserved.
Relative to Truck (5,4): Vector (+1, +2). Behind. Unobserved.
D is Unobserved.

- E (3, 6):
Relative to Door (7,3): Vector (-4, +3).
Angle atan(3/4) = 37 deg.
This is < 45 deg.
So E was seen from Door.
Relative to Truck (5,4): Vector (-2, +2).
Angle 45 deg.
Seen from Truck.
E is Observed.

- B (3, 7):
Relative to Door (7,3): Vector (-4, +4). Angle 45 deg.
Seen from Door.
Relative to Truck (5,4): Vector (-2, +3).
Angle atan(1.5) = 56 deg. > 45.
Not seen from Truck.
But seen from Door!
So B is Observed.

- A (5, 8):
Relative to Door (7,3): Vector (-2, +5). Angle atan(2.5) = 68 deg. > 45. Unobserved.
Relative to Truck (5,4): Vector (0, +4). 90 deg. Unobserved.
A is Unobserved.

- C (3, 4):
Relative to Door (7,3): Vector (-4, +1). Angle atan(1/4) = 14 deg. Inside West cone.
Seen from Door.
Relative to Truck (5,4): Vector (-2, 0). Angle 0.
Seen from Truck.
C is Observed.

Summary:
Unobserved: A, D, F.
Observed: B, C, E.

Wait, let's re-verify F.
F is at (6, 5).
Door at (7, 3).
Vector (-1, 2). Angle ~63 deg to the Right of West.
Agent facing West.
FOV is +/- 45.
63 > 45. So F is "Right" (outside Front-Right bin).
So F is Unseen from Door.
Truck at (5, 4).
F is at (6, 5).
Vector (+1, +1).
Agent facing West.
F is Behind.
So F is Unseen.

Re-verify B.
B is at (3, 7).
Door at (7, 3).
Vector (-4, +4).
Angle 45 degrees.
Is 45 included?
Bins: `(22.5, 45] -> front-right`.
Yes, 45 is included.
So B is Observed.

Re-verify E.
E is at (3, 6).
Door at (7, 3).
Vector (-4, +3).
Angle ~37 deg.
Included.
So E is Observed.

Re-verify A.
A is at (5, 8).
Door (7,3) -> (-2, 5). Angle ~68 deg. Unseen.
Truck (5,4) -> (0, 4). Angle 90 deg. Unseen.
A is Unseen.

Re-verify D.
D is at (6, 6).
Door (7,3) -> (-1, 3). Angle ~71 deg. Unseen.
Truck (5,4) -> (1, 2). Behind. Unseen.
D is Unseen.

So Unexplored: A, D, F.

Wait, let's look at the map "unexplored" definition.
"Select the points that are located in unexplored/unobserved regions."
Maybe I should verify if any walls block the view?
From Door (7,3) to B (3,7). Line of sight passes through (6,4), (5,5), (4,6).
Are there obstacles?
(6,4) is empty `.`
(5,5) is empty `.`
(4,6) is empty `.`
No walls.
What about objects?
Truck is at (5,4).
Line from (7,3) to (3,7)?
Roughly...
x goes 7 -> 3. y goes 3 -> 7.
Midpoint (5, 5).
Truck is at (5, 4).
Close, but maybe doesn't block.
So B is likely seen.

What about A?
Definitely out of angle.

What about F?
Definitely out of angle.

What about D?
Definitely out of angle.

So A, D, F.

Wait, did I miss anything in the prompt about "Observe" behavior?
"When you are at a door, you can see objects from both connected rooms (within FOV)."
I was at Red Door. I observed.
I saw "rubberduck: front-slight-right... truck: front-right... lamp: front-right".
"front-right" is (22.5, 45].
"front-slight-right" is (0, 22.5].
So I saw objects in the 0-45 degree range (North West).
B (angle 45) and E (angle 37) are in this direction.
So they are in the observed region.
F (angle 63) is NOT.

So {A, D, F} seems correct.

Let's check if there are other points.
Map has A, B, C, D, E, F.
Result: A, D, F.

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

THINK:
I am currently at the 'truck' in Room 2 (West room).
Initial position was (0,0) in Room 1 (Center).
Room 1 is connected to Room 2 (West) via the red door.
I moved West to the red door, then jumped to the truck which was front-right (relative to West facing, so North-West) from the door.
Looki...

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

You jumped to truck. You observe:
• rubberduck: front, mid distance, facing right
• lamp: front-right, slightly far.
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 truck. You observe:
• rubberduck: front, mid distance, facing right
• lamp: front-right, slightly far.
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 truck in Room 2. I am facing West (orientation hasn't changed since jump).
I see the rubberduck in front (West) and lamp to the front-right (North-West).
I haven't scanned the South or East directions from inside this room properly (though East is back towards the red door).
I need to check the other directions in Room 2 to make sure there are no other doors or objects.
I'll rotate 90 degrees clockwise to face North.

I am at the truck in Room 2. I am facing West (orientation hasn't changed since jump).
I see the rubberduck in front (West) and lamp to the front-right (North-West).
I haven't scanned the South or East directions from inside this room properly (though East is back towards the red door).
I need to ch...

THINK:
I need to construct the cognitive map based on my trajectory and observations.

**Trajectory & Coordinates Estimation:**
1. **Start (Room 1):** Pos (0,0), Facing North.
* Observed North: Lego man (front-left, slightly far). Let's estimate coordinates. "Front-left" means NW. "Slightly far" is (4,8]. Let's say (-3, 5). Facing backward (South).
2. **Rotate 90 (Facing East):**
* Observed East: Green door (front, near). "Near" is (0,2]. Let's say (2, 0). On front wall.
3. **Rotate 90 (Facing South):**
* Observed South: Backpack (front-right, mid), Shopping cart (front-left, mid).
* Facing South, front-right is SW. Front-left is SE.
* Backpack: SW relative to agent(0,0). Approx (-2, -3). Facing forward (South).
* Shopping cart: SE relative to agent(0,0). Approx (2, -3). Facing Right (East).
4. **Rotate 90 (Facing West):**
* Observed West: Bike (front-slight-right, mid), Lego man (front-right, slightly far), Red door (front, slightly far).
* Facing West, front is West. Front-slight-right is WNW. Front-right is NW.
* Red door: West, slightly far (4,8]. Let's say (-5, 0).
* Bike: WNW. Approx (-4, 1). Facing Left (West).
* Lego man: NW. Consistent with previous sighting.
5. **Jump to Red door:**
* Agent Pos: Approx (-5, 0). Facing West.
* Observed: Rubberduck (front-slight-right, slightly far), Truck (front-right, mid), Lamp (front-right, slightly far).
* Facing West.
* Front-slight-right is WNW. Rubberduck approx (-5 + dx, 0 + dy). Let's say (-10, 2).
* Front-right is NW. Truck (mid, 2-4m). Say (-7, 2). Lamp (slightly far). Say (-9, 3).
6. **Jump to Truck:**
* Agent Pos: (-7, 2). Facing West.
* Observed: Rubberduck (front, mid). Front is West. Rubberduck is west of truck. Confirms relative pos. Lamp (front-right, slightly far). NW of truck.
7. **Rotate 90 (Facing North):**
* Agent Pos: (-7, 2). Facing North.
* Observed: Soda can (front, near). North of truck. Say (-7, 4). Lamp (front-left, slightly far). NW of truck. Consistent.

**Coordinate Consolidation (Integers):**
* **Agent:** Currently at Truck position (-7, 2). Facing North.
* **Lego man:** Room 1. NW of (0,0). Say (-3, 4). Facing South.
* **Green door:** Room 1. East of (0,0). Say (2, 0).
* **Backpack:** Room 1. SW of (0,0). Say (-2, -3). Facing South.
* **Shopping cart:** Room 1. SE of (0,0). Say (2, -3). Facing East.
* **Bike:** Room 1. WNW of (0,0). Say (-4, 1). Facing West.
* **Red door:** Between Room 1 and Room 2. West of (0,0). Say (-5, 0).
* **Truck:** Room 2. NW of Red door. Agent is here (-7, 2). Facing South (backward relative to what? Observe 1 said "facing backward". If truck faces backward, and usually front is forward... let's assume standard object orientation or just record "south" if "backward" means towards South). Wait, the observation said "truck: front-right, mid distance, facing backward". This was from the door facing West. Front-right is NW. So truck is at NW. "Facing backward" relative to the viewer or the object? Usually egocentric object descriptions. If I am looking West, backward is East. So truck faces East? Let's assume cardinal mapping: If agent faces West, backward is East.
* **Rubberduck:** Room 2. West of Truck. Say (-10, 2). From Truck (facing W), duck was front (W). Facing Right -> North.
* **Lamp:** Room 2. NW of Truck. Say (-9, 4).
* **Soda can:** Room 2. North of Truck (near). Say (-7, 4).

Refining coordinates for consistency:
Origin (0,0).
Green Door: (2,0)
Red Door: (-5,0)
Lego Man: (-3, 4)
Backpack: (-2, -3)
Shopping Cart: (2, -3)
Bike: (-4, 1)

At Red Door (-5,0), facing West.
Truck: Front-Right (NW) mid (approx 2.8m). (-7, 2).
Jump to Truck (-7, 2). Facing West.
Rubberduck: Front (West) mid. (-10, 2). Facing North.
Lamp: Front-Right (NW). (-9, 4).
Rotate to North.
Soda can: Front (North) near. (-7, 4).

Object Facings:
Lego man: observed facing "backward" from South view (Wait, observation 1 facing North saw lego man facing "backward"). If agent faces North, backward is South. So Lego man faces South.
Backpack: observed facing "forward" from South view. Agent faces South. Forward is South. Backpack faces South.
Shopping cart: observed facing "right" from South view. Agent faces South. Right is West. Shopping cart faces West. (Wait, description says "facing right" - right of agent facing South is West. Correct.)
Bike: observed facing "left" from West view. Agent faces West. Left is South. Bike faces South.
Truck: observed facing "backward" from West view (at door). Agent faces West. Backward is East. Truck faces East.
Rubberduck: observed facing "right" from West view (at truck). Agent faces West. Right is North. Rubberduck faces North.
Soda can: No facing given.
Lamp: No facing given.

Wait, check shopping cart again. "facing right". From South facing agent. Right of South is West. Yes.
Check bike again. "facing left". From West facing agent. Left of West is South. Yes.

Let's double check observations.
Obs 1 (Face N): Lego man facing backward (South).
Obs 3 (Face S): Backpack facing forward (South). Shoppingcart facing right (West).
Obs 4 (Face W): Bike facing left (South). Lego man facing left (South). Wait. Obs 1 said backward (South). Obs 4 said left (South). Consistent.
Obs 5 (Face W at door): Rubberduck facing right (North). Truck facing backward (East).
Obs 6 (Face W at truck): Rubberduck facing right (North).
Obs 7 (Face N at truck): Soda can (no facing).

Current Agent State: Position of Truck (-7, 2), Facing North.

FINAL ANSWER:
```json
{
"agent": {"position": [-7, 2], "facing": "north"},
"lego man": {"position": [-3, 4], "facing": "south"},
"green door": {"position": [2, 0]},
"backpack": {"position": [-2, -3], "facing": "south"},
"shoppingcart": {"position": [2, -3], "facing": "west"},
"bike": {"position": [-4, 1], "facing": "south"},
"red door": {"position": [-5, 0]},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-10, 2], "facing": "north"},
"lamp": {"position": [-9, 4]},
"soda can": {"position": [-7, 4]}
}
```

THINK:
I need to construct the cognitive map based on my trajectory and observations.

**Trajectory & Coordinates Estimation:**
1. **Start (Room 1):** Pos (0,0), Facing North.
* Observed North: Lego man (front-left, slightly far). Let's estimate coordinates. "Front-left" means NW. "Slightly f...

{
  "agent": {
    "position": [
      -7,
      2
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      4
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      -4,
      1
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -10,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -9,
      4
    ]
  },
  "soda can": {
    "position": [
      -7,
      4
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "north"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "north"
  }
}

THINK:
I am currently at the 'truck' in Room 2. My global orientation is North (since I faced West at the red door, jumped to truck without rotation, then rotated 90 degrees clockwise). Wait, let's trace:
1. Start (0,0) facing North.
2. Rotate 90 -> Face East.
3. Rotate 90 -> Face South.
4. Rotate 90 -> Face West. Jump to Red Door. Face West.
5. Jump to Truck. Face West.
6. Rotate 90. Face North.

Current state: At 'truck', facing North (global).
Local frame: +y is North, +x is East.

Current Observation:
- soda can: front, near.
- "Front" means along +y axis. "Near" is (0,2]. Let's say y=2. Position relative to agent: [0, 2].
- No facing info provided for soda can.
- lamp: front-left, slightly far.
- "Front-left" is between North and West. 45 degrees left is North-West.
- "Slightly far" is (4,8]. Let's estimate x=-4, y=4.
- No facing info provided for lamp.

Previous observation from truck (facing West):
- rubberduck: front, mid distance. (Front was West). So relative to North-facing, it is Left (-x).
- lamp: front-right, slightly far. (Front was West, so right is North). This matches the current view where lamp is front-left (North-West) relative to North facing?
- Facing West (old +y): Lamp was front-right (+x, +y relative to West). This is North-West global.
- Facing North (new +y): Lamp is front-left (-x, +y relative to North). This is North-West global. Consistency check passed.

I need to output the Local Cognitive Map based *only* on the current `Observe()` output.
Current Observe:
- soda can: front, near.
- lamp: front-left, slightly far.

Local coordinates (relative to agent facing North):
- soda can: Front -> (0, y). Near -> dist ~ 1-2. Let's pick [0, 2].
- lamp: Front-left -> (-x, y). Slightly far -> dist ~ 5-6. Let's pick [-4, 4].

The JSON schema requires relative positions.

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"soda can": {"position": [0, 2]},
"lamp": {"position": [-4, 4]}
}
}

THINK:
I am currently at the 'truck' in Room 2. My global orientation is North (since I faced West at the red door, jumped to truck without rotation, then rotated 90 degrees clockwise). Wait, let's trace:
1. Start (0,0) facing North.
2. Rotate 90 -> Face East.
3. Rotate 90 -> Face South.
4. Rotate 9...

{
  "origin": "agent",
  "objects": {
    "soda can": {
      "position": [
        0,
        2
      ]
    },
    "lamp": {
      "position": [
        -4,
        4
      ]
    }
  }
}

{
  "lamp": {
    "position": [
      -4,
      4
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      0,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "soda can": {
      "position": [
        0,
        2
      ]
    },
    "lamp": {
      "position": [
        -4,
        4
      ]
    }
  }
}

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

You rotated clockwise 90°. You observe:
• soda can: front, near
• lamp: front-left, 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:
• soda can: front, near
• lamp: front-left, 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 truck, facing North.
I see a soda can (near, front) and the lamp (front-left).
I have not seen the South or West sectors fully from this position yet (though I saw West previously).
I need to check East and South. East should face back towards the red door. South is unexplored from this spot.
Let's rotate 90 clockwise to face East to confirm the door's location relative to the truck and check for other things.

I am at the truck, facing North.
I see a soda can (near, front) and the lamp (front-left).
I have not seen the South or West sectors fully from this position yet (though I saw West previously).
I need to check East and South. East should face back towards the red door. South is unexplored from this ...

THINK:
I need to synthesize the cognitive map based on my observations.

**Trajectory & Coordinates:**
1. **Start (Room 1):** (0,0), facing North.
* Observe North: Lego man (front-left, slightly far, facing backward).
* "Slightly far" is (4,8]. Front-left is approx -45 to -22.5 deg.
* Let's estimate Lego man position. Distance ~6. Angle ~-30.
* (0,0) facing N. Lego man is roughly (-3, 5).
2. **Rotate 90 (Face East):**
* Observe East: Green door (front, near, on front wall).
* "Near" is (0,2]. Front is East.
* Green door position: approx (2, 0).
3. **Rotate 90 (Face South):**
* Observe South: Backpack (front-right, mid), Shopping cart (front-left, mid).
* Backpack: facing S, front-right (SW). Distance (2,4] -> ~3. Angle ~+30 (S->W). Position: (-1.5, -2.5). Facing forward -> S.
* Shopping cart: facing S, front-left (SE). Distance (2,4] -> ~3. Angle ~-30 (S->E). Position: (1.5, -2.5). Facing right -> W.
* Relative: Backpack is East of Shopping cart? No, wait.
* Agent facing South. Front-Right is West (Agent's right). Front-Left is East (Agent's left).
* Observation says: "backpack: front-right... shoppingcart: front-left".
* So Backpack is to the West-ish. Shopping cart is to the East-ish.
* Relative check: "backpack is east, near to shoppingcart."
* This contradicts the ego-centric description if facing South.
* If facing South: Right is West. Left is East.
* Backpack at Front-Right -> South-West.
* Shopping cart at Front-Left -> South-East.
* So Backpack should be West of Shopping cart.
* But relative text says "backpack is east... to shoppingcart". This is a conflict.
* Usually ego-centric is more reliable for raw position. Let's assume standard definitions.
* Maybe "backpack: front-right" means relative to North? No, "Observe action only reports from your current position and facing direction."
* Let's assume the relative text meant "Backpack is west of shopping cart"? Or maybe I got the ego-centric mapping wrong.
* Wait, let's look at the example or rules.
* Orientation: "right" (ego) when facing South is West. "left" is East.
* So Backpack (front-right) is South-West. ShoppingCart (front-left) is South-East.
* This places Shopping Cart to the East of Backpack.
* The relative text "backpack is east, near to shoppingcart" implies B is East of S.
* Let's hold off on precise coords and use rough topology. Backpack/Cart are South.
4. **Rotate 90 (Face West):**
* Observe West: Bike (front-slight-right, mid), Lego man (front-right, slightly far), Red door (front, slightly far).
* Facing West.
* Red door: Front -> West. Slightly far (4,8] -> ~6. Pos: (-6, 0).
* Lego man: Front-right -> North-West. Seen before from (0,0) facing N as front-left. Consistent. Pos ~(-3, 5).
* Bike: Front-slight-right -> West-North-West. Mid distance (2,4] -> ~3. Pos: (-3, 1).
5. **Jump to Red Door:**
* Jump from (0,0) to Red door at ~(-6, 0). Agent now at Red door.
* Facing West.
* Observe: Rubberduck (front-slight-right, slightly far), Truck (front-right, mid), Lamp (front-right, slightly far).
* Facing West. Front-right is North-West.
* Truck: Mid (2,4] -> ~3. Angle ~45. Pos relative to door: (-2, 2). Global: (-8, 2).
6. **Jump to Truck:**
* Jump from Red door ~(-6,0) to Truck ~(-8, 2).
* Facing West.
* Observe: Rubberduck (front, mid), Lamp (front-right, slightly far).
* Rubberduck: Front (West). Mid distance ~3. Truck is at (-8,2). Duck ~(-11, 2).
* Lamp: Front-right (NW). Slightly far ~6. Lamp ~(-8-4, 2+4) = (-12, 6)?
* Previous observation from Door: Lamp was front-right (NW). Consistent.
7. **Rotate 90 (Face North):**
* At Truck ~(-8, 2).
* Observe: Soda can (front, near), Lamp (front-left, slightly far).
* Facing North.
* Soda can: Front (North). Near ~1-2. Pos: (-8, 4).
* Lamp: Front-left (NW). Consistent.
8. **Rotate 90 (Face East):**
* At Truck ~(-8, 2).
* Observe: Red door (front-right, mid).
* Facing East.
* Front-right is South-East.
* Red door is at (-6, 0).
* Truck is (-8, 2).
* Vector T->D is (2, -2).
* Facing East (1, 0). Vector (2, -2) is roughly -45 degrees (Right).
* "Front-right" fits perfectly.
* Mid distance: sqrt(8) ~ 2.8. Fits (2,4].

**Coordinates Calculation:**
Let's refine coordinates.
- **Agent Start:** (0,0).
- **Green Door:** East, near. Let's say (2, 0).
- **Red Door:** West, slightly far. Range 4-8. Let's pick 5 or 6. Let's say (-5, 0).
- **Lego Man:** From (0,0) facing N -> Front-left (-45 to -22.5). Slightly far (4-8).
From (0,0) facing W -> Front-right (NW). Slightly far.
Intersection suggests (-3, 4) or similar.
- **Bike:** From (0,0) facing W -> Front-slight-right (WNW). Mid (2-4).
Let's say (-3, 1).
- **Backpack & Shopping Cart:** South of (0,0).
Backpack (SW), Cart (SE). Dist ~3.
Backpack: (-1, -3). Cart: (1, -3).
- **Room 2 (accessed via Red Door at -5,0):**
Agent at Red Door (-5,0), facing West.
Truck: Front-right (NW), mid (2-4). Let's say dx=-2, dy=2. Truck at (-7, 2).
Observation from Truck (facing E) says Door is Front-right (SE). T(-7,2) -> D(-5,0) is (+2, -2). Facing East, +2 is Front, -2 is Right. Front-Right. Matches. Distance sqrt(8)=2.8 (Mid). Perfect.
- **Objects relative to Truck (-7, 2):**
- **Soda Can:** Facing North, "Front, Near". Near is <2. Let's say (0, 1.5) relative.
Global: (-7, 3.5). Round to integers -> (-7, 4) or (-7, 3).
- **Rubberduck:**
From Door (-5,0) facing W: Front-slight-right (WNW), slightly far (4-8).
From Truck (-7,2) facing W: Front (W), mid (2-4).
Let's say Duck is at (-10, 2).
From Door: (-5,0) -> (-10,2) is (-5, 2). Dist sqrt(29)=5.4. Slightly far. Angle: W is (-1,0). (-5,2) is slight right. Matches.
From Truck: (-7,2) -> (-10,2) is (-3, 0). Dist 3. Mid. Front. Matches.
- **Lamp:**
From Door (-5,0) facing W: Front-right (NW). Slightly far.
From Truck (-7,2) facing W: Front-right (NW). Slightly far.
From Truck (-7,2) facing N: Front-left (NW). Slightly far.
Let's say Lamp is at (-11, 5).
From Door: (-6, 5). Dist ~8. Front-right.
From Truck: (-4, 3). Dist 5. Front-right (if facing W), Front-left (if facing N). Matches.

**Summary of Objects:**
- Agent: currently at Truck (-7, 2), facing East.
- Green door: (2, 0).
- Red door: (-5, 0).
- Lego man: (-3, 4). Facing: backward (South).
- Bike: (-3, 1). Facing: left (West).
- Backpack: (-1, -3). Facing: forward (North? context was facing S, facing forward -> S). Original: "facing forward". If agent faces S, object facing forward means object faces S.
- Shoppingcart: (1, -3). Facing: right (West).
- Truck: (-7, 2). Facing: backward (East? From door facing W, truck facing backward -> East).
- Soda can: (-7, 4).
- Rubberduck: (-10, 2). Facing: right (North? From door facing W, facing right -> North).
- Lamp: (-11, 5).

Let's check facing directions provided in observations:
- Lego man: facing backward (relative to agent facing N -> South).
- Green door: on front wall (relative to agent facing E -> wall normal points W? Door usually connects. Let's just list position).
- Backpack: facing forward (relative to agent facing S -> South).
- Shoppingcart: facing right (relative to agent facing S -> West).
- Bike: facing left (relative to agent facing W -> South).
- Red door: on front wall (relative to agent facing W).
- Truck: facing backward (relative to agent facing W -> East).
- Rubberduck: facing right (relative to agent facing W -> North).

Refining coordinates to integers:
- Agent start (0,0).
- Green door (2,0).
- Red door (-5,0).
- Lego man (-3,4).
- Bike (-3,1).
- Backpack (-2,-3).
- Shoppingcart (2,-3).
- Truck (-7,2).
- Soda can (-7,4).
- Rubberduck (-10,2).
- Lamp (-11,6).

Wait, the prompt says "Minimize total COST". I shouldn't just map, I need to finish. But for this specific turn, I just need the output.
I need to query if uncertain? No, coordinates seem consistent enough for a topological map.
I'll stick to the integer grid estimation.

One conflict: "Assume your current facing direction is called 'north': backpack is east, near to shoppingcart."
My estimation: Backpack (-2,-3), Shoppingcart (2,-3). Backpack is West of Shoppingcart.
Agent was facing South.
Agent's "North" (current facing) is Global South.
Agent's "East" (current right) is Global West.
So "Backpack is 'east'" means Backpack is Global West of ... something?
"backpack is east, near to shoppingcart" -> In agent's relative frame (North=Global South, East=Global West), Backpack is East (Global West) of Shoppingcart.
So Global West of Shoppingcart.
My coords: Backpack (-2, -3) is West of Cart (2, -3). This matches the relative description.
So the coordinates are likely correct.

Refined list:
- agent: (-7, 2), facing East.
- green door: (2, 0).
- red door: (-5, 0).
- lego man: (-3, 4), facing South.
- bike: (-3, 1), facing South.
- backpack: (-2, -3), facing South.
- shoppingcart: (2, -3), facing West.
- truck: (-7, 2), facing East.
- soda can: (-7, 4).
- rubberduck: (-10, 2), facing North.
- lamp: (-11, 5).

FINAL ANSWER:
```json
{
"agent": {"position": [-7, 2], "facing": "east"},
"green door": {"position": [2, 0]},
"red door": {"position": [-5, 0]},
"lego man": {"position": [-3, 4], "facing": "south"},
"bike": {"position": [-3, 1], "facing": "south"},
"backpack": {"position": [-2, -3], "facing": "south"},
"shoppingcart": {"position": [2, -3], "facing": "west"},
"truck": {"position": [-7, 2], "facing": "east"},
"soda can": {"position": [-7, 4]},
"rubberduck": {"position": [-10, 2], "facing": "north"},
"lamp": {"position": [-11, 5]}
}
```

THINK:
I need to synthesize the cognitive map based on my observations.

**Trajectory & Coordinates:**
1. **Start (Room 1):** (0,0), facing North.
* Observe North: Lego man (front-left, slightly far, facing backward).
* "Slightly far" is (4,8]. Front-left is approx -45 to -22.5 deg....

{
  "agent": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "lego man": {
    "position": [
      -3,
      4
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "west"
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      4
    ]
  },
  "rubberduck": {
    "position": [
      -10,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -11,
      5
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  }
}

THINK:
I need to generate a Local Cognitive Map based on my current observation.
Current state:
- Location: At the 'truck'.
- Orientation: Facing East (rotated 90 clockwise from North).
- Observation: "red door: front-right, mid distance, on front wall."

Wait, the previous observation when facing East was: "red door: front-right, mid distance, on front wall."
Wait, I am at the truck. I rotated to face East.
"front-right" relative to Facing East means roughly South-East.
Wait, if I am facing East, front is East, right is South. Front-right is South-East.
"mid distance" usually implies a distance between 2 and 4.
Let's estimate coordinates.
Agent is at (0,0) locally facing +y (East).
Red door is front-right (angle 45 deg clockwise roughly).
So local coordinates: x > 0, y > 0?
No, "front" is +y. "right" is +x.
Front-right is roughly (+x, +y).
Wait, angle bins:
(22.5, 45] is front-right.
So it is mostly front, slightly right? Or diagonal?
Usually 45 degrees is diagonal.
Let's assume roughly x=2, y=3 or similar for mid distance (~3.5).
Wait, the door is "on front wall". This usually implies the wall I am facing.
If I am facing East, the front wall is the East wall.
Position of door:
If it's on the front wall, but front-right direction, it means it's to the right of the center of my view.
Let's assign reasonable local coordinates.
Distance ~3.
Angle ~30-40 degrees.
x = 3 * sin(30) = 1.5 -> 2
y = 3 * cos(30) = 2.5 -> 3
So maybe [2, 3] relative to agent.
But wait, the orientation of the door is "on front wall".
The agent is facing East (+y in local frame).
Front wall is at some +y distance.
If the door is on the front wall, it's facing towards the agent (or away?).
Doors on walls usually face perpendicular to the wall.
If the wall is East, the door faces West.
In local frame (where +y is East), West is -y.
So door facing is "-y".

Let's refine the position.
"front-right" -> x > 0, y > 0.
Let's assume local pos [2, 3] or similar.
Let's stick to the observed data.
Object: red door.
Properties: front-right, mid distance.
Facing: "on front wall".
If I face East, and see it on the front wall, the wall is perpendicular to my view, so the wall runs North-South. The door is on it.
So the door faces West (back at me).
West is -y in local frame.

Constructing JSON:
Origin: agent
Objects: red door
Position: [x, y]. Let's say [1, 3] (front-right).
Facing: "-y" (facing back towards agent).

Wait, I should verify the "facing" of the door.
Instruction: "Gate's orientation: report wall position (e.g., 'on left wall')."
My observation says "on front wall".
The schema asks for facing in "+x|-x|+y|-y".
If the door is on the front wall relative to me (facing +y), then the door's normal is likely -y (facing me).

Let's verify the objects. Only "red door" was reported in the last Observe().
"soda can" and "lamp" were in the previous observation (facing North).
The current observation only mentions "red door".

So the map should only contain "red door".

Coordinates:
Distance "mid" -> ~3 units.
Front-right -> +x, +y.
Let's approximate [1, 3] or [2, 2].
Let's use [2, 3].
Facing: "-y".

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

THINK:
I need to generate a Local Cognitive Map based on my current observation.
Current state:
- Location: At the 'truck'.
- Orientation: Facing East (rotated 90 clockwise from North).
- Observation: "red door: front-right, mid distance, on front wall."

Wait, the previous observation when facing E...

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

{
  "red door": {
    "position": [
      1,
      2
    ],
    "facing": "east"
  }
}

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

You rotated clockwise 90°. You observe:
• red door: front-right, mid distance, on front wall.
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:
• red door: front-right, mid distance, on front wall.
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 truck facing East. I see the red door to the front-right.
I have scanned West, North, East. I need to scan South.
I will rotate 90 degrees clockwise to face South.

I am at the truck facing East. I see the red door to the front-right.
I have scanned West, North, East. I need to scan South.
I will rotate 90 degrees clockwise to face South....

THINK:
I need to construct the JSON map based on the observations so far.

**Room 1 Analysis (Origin 0,0, Agent starts facing North):**
- **Initial (0,0, North):**
- `lego man`: front-left (NW), slightly far, facing backward (South). "Slightly far" is (4,8]. Let's estimate position. NW diagonal. Maybe (-4, 4)?
- **(0,0, East):**
- `green door`: front (East), near ((0,2]), on front wall. Let's place it at (2, 0) or (1,0). Since it's a door on a wall, usually grid aligned. Let's assume (2,0).
- **(0,0, South):**
- `backpack`: front-right (SW), mid distance ((2,4]), facing forward (North).
- `shoppingcart`: front-left (SE), mid distance ((2,4]), facing right (East).
- Relation: backpack is East of shoppingcart (wait, "backpack is east, near to shoppingcart").
- From (0,0) facing South: Front-Right is South-West. Front-Left is South-East.
- Backpack at SW: (-2, -2)?
- Shoppingcart at SE: (2, -2)?
- Relation check: Backpack (SW) is East of Shoppingcart (SE)? No, SW is West of SE. Let's re-read the observation.
- "backpack: front-right, mid distance... shoppingcart: front-left". Facing South.
- Front-Right relative to South is West. So Backpack is SW/West.
- Front-Left relative to South is East. So Shoppingcart is SE/East.
- "Assume your current facing direction is called 'north': backpack is east, near to shoppingcart."
- This relative description is confusing. If current facing is "north" (actually South), then "East" relative to "north" is global West.
- So Backpack is West of Shoppingcart. This matches the ego observation (Backpack at Front-Right/West vs Cart at Front-Left/East).
- Let's estimate coords: Shoppingcart (2, -3), Backpack (-2, -3).
- **(0,0, West):**
- `bike`: front-slight-right (NW), mid distance ((2,4]), facing left (South).
- `lego man`: front-right (NW), slightly far, facing left (South). (Consistent with previous).
- `red door`: front (West), slightly far ((4,8]), on front wall. Let's estimate (-5, 0).
- Relation: bike is West of lego man? "bike is west, near to lego man".
- Lego man at (-4, 4). Bike is mid-distance NW. West of Lego man? If Lego is (-4,4), Bike could be (-6, 4) or (-5, 5). "Front-slight-right" from West facing means North-West.

**Room 2 Analysis (Connected via Red Door at ~(-5,0)):**
- Jumped to `red door`. Facing West.
- Observed:
- `rubberduck`: front-slight-right (W-NW), slightly far.
- `truck`: front-right (NW), mid distance ((2,4]).
- `lamp`: front-right (NW), slightly far.
- Jumped to `truck`. Facing West.
- Position of truck relative to door: Door is at ~(-5,0). Truck is NW, mid-dist. Let's say Truck is at (-7, 2).
- At Truck (-7, 2), facing West.
- `rubberduck`: front (West), mid dist. Maybe (-10, 2).
- `lamp`: front-right (NW), slightly far. Maybe (-9, 4).
- Rotated to North (at Truck):
- `soda can`: front (North), near. Maybe (-7, 3) or (-7, 4).
- `lamp`: front-left (NW), slightly far. Consistent.
- Rotated to East (at Truck):
- `red door`: front-right (SE), mid distance.
- Truck at (-7, 2). Red door at (-5, 0). From (-7, 2) facing East, (-5, 0) is roughly South-East (Front-Right). Consistent.
- Rotated to South (at Truck):
- No objects.

**Grid Estimation:**
1. **Agent Start:** (0,0).
2. **Green Door:** East, near. (2,0).
3. **Red Door:** West, slightly far. (-5,0).
4. **Lego Man:** NW of (0,0), slightly far. (~(-4, 4)).
5. **Bike:** West of Lego Man. (~(-6, 4)). Mid distance from (0,0) facing West (NW sector).
6. **Backpack:** SW of (0,0). (~(-2, -3)). Facing North.
7. **Shoppingcart:** SE of (0,0). (~(2, -3)). Facing East.
8. **Truck:** NW of Red Door. Door is (-5,0). Truck is mid-dist NW. Let's map to (-7, 2). Facing Backward (relative to observation from door facing West? No, initial obs: "facing backward").
- From Red Door (facing West), Truck was "facing backward". If "Backward" relative to agent facing West, that's East.
9. **Rubberduck:** West of Truck. Truck (-7,2). Duck mid-dist West. (-10, 2). Facing Right (North).
10. **Lamp:** NW of Truck. Slightly far. (-9, 5).
11. **Soda Can:** North of Truck. Near. (-7, 3).
12. **Agent Current:** At Truck. Facing South.

Let's refine coordinates for integer grid logic.
- Green door: (2,0).
- Red door: (-4,0) or (-5,0). "Slightly far" > 4. So (-5,0) is good.
- Lego man: (-3, 3) or (-4, 4). Front-Left from North. Front-Right from West. (-4, 4) fits "slightly far" (dist 5.6).
- Bike: "West, near to lego man". If Lego is (-4,4), Bike is (-5,4) or (-6,4). "Front-slight-right" from West (facing West at 0,0) -> NW. Dist (2,4]. (-4,4) dist is 5.6 (slightly far). (-3,2) dist 3.6 (mid). Maybe Bike is closer.
- Shoppingcart: Front-Left from South (SE). Mid dist. (2, -3).
- Backpack: Front-Right from South (SW). Mid dist. (-2, -3).

Room 2:
- Red door at (-5,0).
- Truck: Front-Right (NW) from door facing West. Dist (2,4]. dx=-2, dy=2 -> (-7, 2). Dist 2.8. Matches.
- Rubberduck: Front (West) from Truck (-7,2). Mid dist. (-10, 2).
- Lamp: Front-Left from Truck facing North (NW). Slightly far. (-9, 5).
- Soda can: Front from Truck facing North. Near. (-7, 3).

Final check on facings:
- Lego man: facing backward (South).
- Backpack: facing forward (North).
- Shoppingcart: facing right (East).
- Bike: facing left (South).
- Rubberduck: facing right (North).
- Truck: facing backward (East).

Current Agent: At Truck (-7, 2), facing South.

FINAL ANSWER:
```json
{
"agent": {"position": [-7, 2], "facing": "south"},
"green door": {"position": [2, 0], "facing": "east"},
"red door": {"position": [-5, 0], "facing": "west"},
"lego man": {"position": [-4, 4], "facing": "south"},
"bike": {"position": [-6, 4], "facing": "south"},
"backpack": {"position": [-2, -3], "facing": "north"},
"shoppingcart": {"position": [2, -3], "facing": "east"},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-10, 2], "facing": "north"},
"lamp": {"position": [-9, 5]},
"soda can": {"position": [-7, 3]}
}
```

THINK:
I need to construct the JSON map based on the observations so far.

**Room 1 Analysis (Origin 0,0, Agent starts facing North):**
- **Initial (0,0, North):**
- `lego man`: front-left (NW), slightly far, facing backward (South). "Slightly far" is (4,8]. Let's estimate position. NW diagonal. M...

{
  "agent": {
    "position": [
      -7,
      2
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "west"
  },
  "lego man": {
    "position": [
      -4,
      4
    ],
    "facing": "south"
  },
  "bike": {
    "position": [
      -6,
      4
    ],
    "facing": "south"
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "north"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -10,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -9,
      5
    ]
  },
  "soda can": {
    "position": [
      -7,
      3
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "south"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -7,
      1
    ],
    "facing": "south"
  }
}

THINK:
I am at the truck facing South. I observe nothing in my field of view.
This means the area to the South of the truck is empty or contains objects beyond the FOV.
My task now is to output the Local Cognitive Map based *only* on the current observation.
Current observation: "No objects in field of view."
Therefore, the "objects" dictionary should be empty.
The origin is "agent".

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

THINK:
I am at the truck facing South. I observe nothing in my field of view.
This means the area to the South of the truck is empty or contains objects beyond the FOV.
My task now is to output the Local Cognitive Map based *only* on the current observation.
Current observation: "No objects in field...

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

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

You rotated clockwise 90°. You observe: No objects in field of view..
You have a maximum of 11 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe: No objects in field of view..
You have a maximum of 11 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I have scanned all 4 directions from the truck in Room 2.
Objects found in Room 2:
- Rubberduck
- Truck (current pos)
- Lamp
- Soda can
- Red door (connection to Room 1)

I have not found any other doors in Room 2. I have scanned 360 degrees.
Room 1 contained the Red door and Green door.
Room 2 seems to be a dead end connected via the Red door.
Room 3 must be behind the Green door in Room 1.
I need to go back to Room 1 and then to the Green door.
Current position: Truck.
Known path: Truck -> Red door -> Room 1.
I see the Red door from my current position (observed when facing East, currently facing South).
I need to Rotate to face the Red door (East-ish) or just Jump to it if it's in FOV?
Wait, I am facing South. The Red door was "front-right" when I faced East. That means it is roughly South-East? No, if I face East and it's front-right, it's South-East relative to the grid, or relative to me?
"When agent faces north: forward = north, right = east".
Facing East: forward = East, right = South. Front-right = South-East.
So the door is South-East of the truck.
I am facing South. Front is South. Front-left is South-East.
So the door should be in my FOV if I am facing South?
Let's check the previous observation when facing East: "red door: front-right".
My current facing is South.
Relative to South: East is Left. South-East is Front-Left.
So the Red door should be Front-Left.
Wait, my last Observe said "No objects in field of view".
This implies the Red door is NOT in the FOV of South facing.
Why?
Facing East (90 deg): Door is front-right (approx South-East).
Facing South (180 deg): Door should be front-left.
Maybe it is "beyond-fov"? The bins are specific.
If it was (22.5, 45] when facing East, that's -45 to -67.5 relative to East? No, + is clockwise. Front-right is +22.5 to +45.
So direction is East + (22.5 to 45) = 112.5 to 135 degrees.
Facing South is 180 degrees.
Angle difference: (112.5 to 135) - 180 = -67.5 to -45.
This falls into "beyond-fov" or just edge of front-left?
Bins: [-45, -22.5) is front-left.
-45 to -67.5 is strictly left of front-left. It might be outside the [-45, 45] cone?
Wait, "front-left" is [-45, -22.5). "front-slight-left" is [-22.5, 0).
Anything less than -45 is "beyond-fov".
So yes, the door is likely outside the FOV when facing South.
I need to turn to see the red door to jump to it.
I should rotate to face East (where I saw it) or South-East?
I can only rotate in 90 degree increments.
I will rotate -90 (counter-clockwise) to face East again. Then I will see the door.
Then I will jump to the red door.
Wait, I need to minimize steps.
Can I Rotate and Jump in one turn? Yes.
I am facing South. Rotate(-90) makes me face East.
Then JumpTo(red door).
Then Observe().
This moves me to the door.

I have scanned all 4 directions from the truck in Room 2.
Objects found in Room 2:
- Rubberduck
- Truck (current pos)
- Lamp
- Soda can
- Red door (connection to Room 1)

I have not found any other doors in Room 2. I have scanned 360 degrees.
Room 1 contained the Red door and Green door.
Room 2 seem...

THINK:
I need to reconstruct the coordinates of all observed objects based on the observations and movements.

**Step 1: Define Coordinate System**
- Origin (0, 0) is the initial position in Room 1.
- Initial facing: North (+y).
- Directions: North (+y), East (+x), South (-y), West (-x).

**Step 2: Trace Movements and Observations**

**Turn 1:**
- Pos: (0, 0), Facing: North.
- Observe: Lego man (front-left, slightly far, facing backward).
- Front-left: approx -30 to -45 deg. Slightly far: 4-8 units. Let's est (-3, 5).
- Facing backward relative to me (North) means facing South.

**Turn 2:**
- Rotate 90 (Facing East).
- Observe: Green door (front, near, on front wall).
- Front = East. Near = 0-2 units. Let's est (2, 0).
- On front wall relative to East: The wall is vertical (North-South), door faces West? Or passage is East? "On front wall" usually means the wall I'm facing. So the door leads East.

**Turn 3:**
- Rotate 90 (Facing South).
- Observe: Backpack (front-right, mid), Shopping cart (front-left, mid).
- Facing South. Front-right is South-West (approx (-2, -3)). Front-left is South-East (approx (2, -3)).
- Mid distance: 2-4 units.

**Turn 4:**
- Rotate 90 (Facing West).
- Observe: Bike (front-slight-right, mid), Lego man (front-right, slightly far), Red door (front, slightly far).
- Facing West.
- Red door: Front (West). Slightly far (4-8). Let's est (-5, 0).
- Bike: Front-slight-right (West + slight North). Mid (2-4). Approx (-3, 1).
- Lego man: Front-right (North-West). Seen before at (-3, 5). Consistent.

**Turn 5:**
- JumpTo(Red door). Pos: (-5, 0). Facing: West.
- Observe: Rubberduck (front-slight-right, slightly far), Truck (front-right, mid), Lamp (front-right, slightly far).
- Facing West.
- Truck: Front-right (North-West). Mid (2-4). Approx (-7, 2).
- Rubberduck: Front-slight-right (West-North-West). Slightly far (4-8). Approx (-9, 1).
- Lamp: Front-right. Slightly far. Approx (-8, 3).

**Turn 6:**
- JumpTo(Truck). Pos: (-7, 2). Facing: West.
- Observe: Rubberduck (front, mid), Lamp (front-right, slightly far).
- Facing West.
- Rubberduck: Front (West). Mid (2-4). Previous est (-9, 1). From (-7, 2), (-9, 2) is West, dist 2. Let's refine Rubberduck to (-9, 2).
- Lamp: Front-right (North-West). Slightly far. Previous est (-8, 3). From (-7, 2), (-8, 3) is (-1, 1) -> dist 1.4 (near). Wait, observation says "slightly far" (4-8). This is inconsistent.
- Let's re-eval. From Truck (-7, 2) facing West:
- Lamp is Front-right (North-West).
- From Red Door (-5, 0) facing West: Lamp was Front-right (North-West).
- Maybe Lamp is further North? Say (-9, 6).
- From Door (-5, 0): (-4, 6) -> dist ~7. Front-right. Matches.
- From Truck (-7, 2): (-2, 4) -> dist ~4.5. Front-right. Matches.

**Turn 7:**
- Rotate 90 (Facing North). Pos: (-7, 2).
- Observe: Soda can (front, near), Lamp (front-left, slightly far).
- Facing North.
- Soda can: Front (North). Near (0-2). Approx (-7, 3) or (-7, 4).
- Lamp: Front-left (North-West). Slightly far. From (-7, 2), (-9, 6) is (-2, +4). Dist 4.5. Front-left. Matches.

**Turn 8:**
- Rotate 90 (Facing East). Pos: (-7, 2).
- Observe: Red door (front-right, mid).
- Facing East. Front-right is South-East.
- Red door at (-5, 0).
- Vector from (-7, 2) to (-5, 0) is (+2, -2).
- Direction: East + South = South-East. 45 degrees right. Matches Front-right.
- Distance: sqrt(8) ~ 2.8. Mid (2-4). Matches.

**Turn 9:**
- Rotate 90 (Facing South). Pos: (-7, 2).
- Observe: Nothing.

**Turn 10:**
- Rotate -90 (Facing East). JumpTo(Red door). Pos: (-5, 0). Facing: East.
- Observe: Bike (front-left, mid), Backpack (front-right, slightly far), Shopping cart (front-slight-right, slightly far), Green door (front, slightly far).
- Facing East.
- Green door: Front (East). Slightly far (4-8).
- Earlier observation from (0,0) facing East said "Near". (2, 0) from (0,0) is dist 2.
- From (-5, 0) to (2, 0) is dist 7. Fits "slightly far" (4-8). So Green door is at approx (2, 0).
- Bike: Front-left (North-East). Mid (2-4).
- Earlier from (0,0) facing West: Front-slight-right (West-North). Est (-3, 1).
- From (-5, 0) facing East, (-3, 1) is (+2, +1). Dist sqrt(5)~2.2. Front-left (North-East). Matches.
- Backpack: Front-right (South-East). Slightly far.
- From (0,0) facing South: Front-right (South-West). Est (-2, -3).
- From (-5, 0) facing East, (-2, -3) is (+3, -3). Dist sqrt(18)~4.2. Front-right (South-East). Matches.
- Shopping cart: Front-slight-right (East-South). Slightly far.
- From (0,0) facing South: Front-left (South-East). Est (2, -3).
- From (-5, 0) facing East, (2, -3) is (+7, -3). Dist sqrt(58)~7.6. Front-slight-right (East is +7, South is -3 -> angle ~23 deg). Matches.

**Refining Coordinates:**
Agent Current Pos: (-5, 0) [Red Door]. Facing East.

Objects:
- **Red Door**: (-5, 0).
- **Green Door**: (2, 0).
- **Lego Man**: (-3, 5). Facing South (backward relative to North).
- **Bike**: (-3, 1). Facing Left (relative to agent West? Or absolute? Instruction says "facing backward/right/left" is egocentric? No, "facing backward" in Turn 1 was relative to agent facing North. "facing left" in Turn 4 (agent facing West) means object faces South? Or object faces agent's left? The instruction says "Orientation: forward/backward... (ego)".
- Turn 4 (Facing West): Bike facing left. Agent's left is South. So Bike faces South?
- Turn 10 (Facing East): Bike facing right. Agent's right is South. Consistent.
- Bike faces South.
- **Backpack**: (-2, -3).
- Turn 3 (Facing South): Facing forward -> Faces South.
- Turn 10 (Facing East): Facing right -> Faces South. Consistent.
- Backpack faces South.
- **Shopping Cart**: (2, -3).
- Turn 3 (Facing South): Facing right -> Faces West.
- Turn 10 (Facing East): Facing backward -> Faces West. Consistent.
- Shopping Cart faces West.
- **Rubberduck**: (-9, 2).
- Turn 5 (Facing West): Facing right -> Faces North.
- Turn 6 (Facing West): Facing right -> Faces North.
- Rubberduck faces North.
- **Truck**: (-7, 2).
- Turn 5 (Facing West): Facing backward -> Faces East.
- Truck faces East.
- **Lamp**: (-9, 6).
- No facing info given in text (or I missed it? Turn 5: "lamp: front-right, slightly far." Turn 6: "lamp: front-right, slightly far." Turn 7: "lamp: front-left, slightly far." No facing).
- **Soda Can**: (-7, 4).
- Turn 7 (Facing North): Near. No facing.

**Constructing JSON:**
Agent is at (-5, 0), facing East.

Coordinates:
- Agent: [-5, 0], facing east
- Red door: [-5, 0]
- Green door: [2, 0]
- Lego man: [-3, 5], facing south
- Bike: [-3, 1], facing south
- Backpack: [-2, -3], facing south
- Shoppingcart: [2, -3], facing west
- Truck: [-7, 2], facing east
- Rubberduck: [-9, 2], facing north
- Lamp: [-9, 6]
- Soda can: [-7, 4]

Verify distances and descriptions:
- Lego man (-3, 5). From (0,0) facing N: (-3, 5) is front-left (Left 3, Fwd 5 -> angle arctan(-3/5) ~ -31 deg). Matches. Dist sqrt(34)~5.8. Slightly far. Matches.
- Green door (2, 0). From (0,0) facing E: (2, 0) is front. Dist 2. Near. Matches.
- Backpack (-2, -3). From (0,0) facing S: (-2, -3) is front-right (Right 2, Fwd 3). Dist 3.6. Mid. Matches.
- Shoppingcart (2, -3). From (0,0) facing S: (2, -3) is front-left (Left 2, Fwd 3). Dist 3.6. Mid. Matches.
- Bike (-3, 1). From (0,0) facing W: (-3, 1) is front-slight-right (Right 1, Fwd 3). Dist 3.16. Mid. Matches.
- Red door (-5, 0). From (0,0) facing W: (-5, 0) is front. Dist 5. Slightly far. Matches.
- Truck (-7, 2). From (-5, 0) facing W: (-2, 2) is front-right. Dist 2.8. Mid. Matches.
- Rubberduck (-9, 2). From (-5, 0) facing W: (-4, 2) is front-slight-right (Right 2, Fwd 4). Dist 4.5. Slightly far. Matches.
- Lamp (-9, 6). From (-5, 0) facing W: (-4, 6) is front-right. Dist 7.2. Slightly far. Matches.
- Soda can (-7, 4). From (-7, 2) facing N: (0, 2) is front. Dist 2. Near. Matches.

Looks consistent.

FINAL ANSWER:
```json
{
"agent": {"position": [-5, 0], "facing": "east"},
"lego man": {"position": [-3, 5], "facing": "south"},
"green door": {"position": [2, 0]},
"backpack": {"position": [-2, -3], "facing": "south"},
"shoppingcart": {"position": [2, -3], "facing": "west"},
"bike": {"position": [-3, 1], "facing": "south"},
"red door": {"position": [-5, 0]},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-9, 2], "facing": "north"},
"lamp": {"position": [-9, 6]},
"soda can": {"position": [-7, 4]}
}
```

THINK:
I need to reconstruct the coordinates of all observed objects based on the observations and movements.

**Step 1: Define Coordinate System**
- Origin (0, 0) is the initial position in Room 1.
- Initial facing: North (+y).
- Directions: North (+y), East (+x), South (-y), West (-x).

**Step 2: ...

{
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "lego man": {
    "position": [
      -3,
      5
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -9,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -9,
      6
    ]
  },
  "soda can": {
    "position": [
      -7,
      4
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  }
}

THINK:
I am currently located at the **red door** (which connects Room 1 and Room 2).
I just jumped to the red door from inside Room 2 (the truck).
The red door is on the boundary.
My last action was `Rotate(-90), JumpTo(red door), Observe()`.
I was facing South at the truck, rotated -90 to face East.
So I arrived at the red door facing **East**.
The observation is:
- bike: front-left, mid distance, facing right.
- backpack: front-right, slightly far, facing right.
- shoppingcart: front-slight-right, slightly far, facing backward.
- green door: front, slightly far, on front wall.

Coordinate frame (Local):
Origin = Agent (at red door).
+y = East (Agent's facing).
+x = South (Right of East).
-x = North (Left of East).
-y = West (Back).

Mapping objects to local (x, y):
Distance bins:
- near: ~1-2
- mid distance: ~3-4
- slightly far: ~5-8

1. **green door**: "front", "slightly far".
- Direction: Front (+y).
- Distance: ~6 (slightly far is 4-8). Let's estimate 6.
- Local Pos: (0, 6).
- "on front wall" implies facing opposite to me? Or facing the same way? Usually doors on walls face into the room or out. If I see it "on front wall", I am looking at it. I am facing East. The door is on the East wall of Room 1?

2. **bike**: "front-left", "mid distance".
- Direction: Front-left. Angle approx 45 deg left.
- Distance: ~3 (mid is 2-4).
- Local Pos: x < 0, y > 0. Say (-2, 2).
- Facing: "facing right". "Right" in ego frame means East? Or relative to the object? The instruction says "facing right" is an ego-relative description? No, "facing backward", "facing right" usually refers to the object's intrinsic facing relative to the agent's view or global?
- Instruction: "Orientation: -forward/backward/right/left (ego)... When agent faces north: forward = north...".
- "facing right": Object is facing the agent's right.
- Agent faces East. Agent's right is South. So object faces South.
- Local facing: South is +x. So facing "+x".

3. **backpack**: "front-right", "slightly far".
- Direction: Front-right.
- Distance: ~5-6.
- Local Pos: x > 0, y > 0. Say (4, 4).
- Facing: "facing right". Agent faces East. Right is South. Object faces South (+x).

4. **shoppingcart**: "front-slight-right", "slightly far".
- Direction: Front-slight-right. Small x, large y.
- Distance: ~5-6.
- Local Pos: x > 0, y > 0. Say (2, 5).
- Facing: "facing backward". Agent faces East. Backward is West. Object faces West (-y).

5. **Relation**: "backpack is south, near to shoppingcart".
- In global frame (assuming current facing is "north" for the relation report? No, "Assume your current facing direction is called 'north'").
- If current (East) is North:
- Backpack is East (Global South is Agent's Right).
- Relation says: "backpack is south". This uses cardinal directions relative to the "current facing = north" assumption.
- So "South" means "Behind" the agent? Or is it reporting true cardinal relation?
- "Proximity: relations between close objects... Use cardinal directions".
- The text says: "Assume your current facing direction is called 'north': backpack is east...". Wait, the prompt output text says: "Assume your current facing direction is called 'north': backpack is south...".
- Let's re-read the observation text: "Assume your current facing direction is called 'north': • backpack is south, near to shoppingcart."
- If Agent Fwd = North. Then Backpack is South of Shopping Cart.
- Agent Fwd = East (Global).
- So Backpack is West of Shopping Cart (Global).
- Let's check positions.
- Backpack: front-right (South-East in Global?).
- Shoppingcart: front-slight-right (East-ish, slight South).
- If Backpack is South-East and Cart is East-ish.
- Backpack is "South" of Cart in the relative frame?
- Relative frame: North = East (Global). South = West (Global).
- So Backpack is West of Cart?
- Let's look at the "front-right" vs "front-slight-right".
- Front-right is more to the right (South). Front-slight-right is less to the right (closer to East).
- So Backpack has more "South" component (Global) than Cart?
- Wait. "Right" is South (Global).
- If Backpack is Front-Right, it is (East + South).
- If Cart is Front-Slight-Right, it is (East + little South).
- So Backpack is more South than Cart.
- In the relative frame (North=East, East=South), "South" means "West" (Global)? No.
- Relative North = Agent Fwd.
- Relative East = Agent Right.
- Relative South = Agent Back.
- Relative West = Agent Left.
- "Backpack is South...". This means Backpack is "Behind" relative to the Cart in the "North=AgentFwd" frame?
- Or is it "South" in the standard map sense, but the preamble says "Assume...".
- Let's trust the "front-right" labels more.
- Backpack (more right) vs Cart (less right).
- Right = +x (Local).
- Backpack x > Cart x.
- Distances are similar ("slightly far").
- So Backpack is to the right of Cart.
- In relative frame (North=Fwd, East=Right), "East" is Right. "South" is Back.
- If "backpack is south... to shoppingcart", it means Backpack has smaller Y (local) than Cart?
- Let's check: Backpack (front-right) vs Cart (front-slight-right).
- "Front-right" is usually 22.5-67.5 deg. "Front-slight-right" is 0-22.5 deg.
- So Backpack has a wider angle.
- If distances are equal, Backpack has smaller Y and larger X.
- So Backpack is "behind" and "right" of Cart?
- "South" relative to "North=Fwd" is "Back".
- So yes, Backpack is "South" (Back/ -y relative) of Shopping Cart. This matches the angle geometry.

JSON Construction:
Origin: "agent"
Objects:
- bike: pos [-2, 3] (front-left, mid), facing "+x" (facing right -> local right = +x).
- backpack: pos [3, 5] (front-right, slightly far), facing "+x" (facing right).
- shoppingcart: pos [1, 6] (front-slight-right, slightly far), facing "-y" (facing backward).
- green door: pos [0, 7] (front, slightly far), facing "-y" (on front wall -> facing back at me).

Refining coordinates:
Distance "mid" ~3. "slightly far" ~6.
Bike: front-left. Angle ~45. x = -3*sin(45) ~ -2. y = 3*cos(45) ~ 2. Let's say (-2, 2).
Green door: front. x=0, y=6.
Backpack: front-right. Angle ~45. x=4, y=4.
Shoppingcart: front-slight-right. Angle ~15. x=1.5, y=5.8. Say (1, 6).
Check relation: Backpack (4, 4) vs Cart (1, 6).
Backpack is (dx=3, dy=-2) relative to Cart.
Relative frame (North=+y): Backpack is South (dy<0) and East (dx>0) of Cart.
The description says "backpack is south, near to shoppingcart".
Matches dy<0.

Final positions for JSON:
bike: [-2, 2], facing "+x"
backpack: [4, 4], facing "+x"
shoppingcart: [1, 6], facing "-y"
green door: [0, 6], facing "-y"

Wait, "green door... on front wall". A door on the front wall usually represents the passage.
Facing "-y" means it faces the agent.

One more check: "bike... facing right".
Agent faces East. Right is South.
In local frame, +x is Right.
So facing "+x".

"shoppingcart... facing backward".
Agent faces East. Backward is West.
In local frame, -y is Backward.
So facing "-y".

"backpack... facing right".
Facing "+x".

The map looks consistent.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"green door": {"position": [0, 6], "facing": "-y"},
"bike": {"position": [-2, 2], "facing": "+x"},
"backpack": {"position": [4, 4], "facing": "+x"},
"shoppingcart": {"position": [1, 6], "facing": "-y"}
}
}
```

THINK:
I am currently located at the **red door** (which connects Room 1 and Room 2).
I just jumped to the red door from inside Room 2 (the truck).
The red door is on the boundary.
My last action was `Rotate(-90), JumpTo(red door), Observe()`.
I was facing South at the truck, rotated -90 to face Eas...

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        0,
        6
      ],
      "facing": "-y"
    },
    "bike": {
      "position": [
        -2,
        2
      ],
      "facing": "+x"
    },
    "backpack": {
      "position": [
        4,
        4
      ],
      "facing": "+x"
    },
    "shoppingcart": {
      "position": [
        1,
        6
      ],
      "facing": "-y"
    }
  }
}

{
  "backpack": {
    "position": [
      2,
      4
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      0,
      7
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      -1,
      2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      6
    ],
    "facing": "west"
  }
}

{
  "origin": "agent",
  "objects": {
    "green door": {
      "position": [
        0,
        6
      ],
      "facing": "-y"
    },
    "bike": {
      "position": [
        -2,
        2
      ],
      "facing": "+x"
    },
    "backpack": {
      "position": [
        4,
        4
      ],
      "facing": "+x"
    },
    "shoppingcart": {
      "position": [
        1,
        6
      ],
      "facing": "-y"
    }
  }
}

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

You rotated counterclockwise 90°. You jumped to red door. You observe:
• bike: front-left, mid distance, facing right
• backpack: front-right, slightly far, facing right
• shoppingcart: front-slight-right, slightly far, facing backward
• green door: front, slightly far, on front wall
Assume your cu...

I am back at the red door, facing East (into Room 1).
I see the green door "front, slightly far, on front wall".
I need to go to Room 3, which is behind the green door.
I can jump directly to the green door from here as it is in my FOV and I have observed it.
I will JumpTo(green door).
Then I will Observe() to see into Room 3.

I am back at the red door, facing East (into Room 1).
I see the green door "front, slightly far, on front wall".
I need to go to Room 3, which is behind the green door.
I can jump directly to the green door from here as it is in my FOV and I have observed it.
I will JumpTo(green door).
Then I will O...

THINK:
I need to construct the cognitive map based on my observations.
Initial state: Agent at (0,0) facing North in Room 1.
1. Observe at (0,0) facing N:
- Lego man: front-left, slightly far. Front-left is NW. Dist bins: near(0-2), mid(2-4), sl.far(4-8). "Slightly far" ~ 4-8.
Let's estimate. Facing N (0,1). Lego man is NW. Let's say (-2, 2) or (-3, 3).
- "facing backward" -> facing South.

2. Rotate 90 (Face East).
- Green door: front, near. Front is East. Near is (0-2). So Green door is at (2,0) or (1,0). Let's pick (2,0) for "near" usually implies adjacent but distinct. "on front wall" -> wall is East.

3. Rotate 90 (Face South).
- Backpack: front-right (SW), mid dist (2-4). Facing forward (South).
- Shopping cart: front-left (SE), mid dist. Facing right (West).
- "backpack is east, near to shoppingcart". Wait, "Assume your current facing direction is called north". Current is South. So relative North is South. Relative East is West.
So "backpack is relative-east (West) of shoppingcart".
Backpack is SW. Shopping cart is SE. West of SE is SW. That matches.
Positions: South is -y.
Backpack (SW): (-2, -2)?
Shopping cart (SE): (2, -2)?

4. Rotate 90 (Face West).
- Bike: front-slight-right (NW-ish), mid dist. Facing left (South).
- Lego man: front-right (NW), sl. far. Facing left (South).
- Red door: front (West), sl. far (4-8). "on front wall".
- "bike is west, near to lego man".
Lego man was NW. Bike is NW. Bike is West of Lego man?
Facing West: front is West. Right is North.
Bike: front-slight-right -> West-North-West.
Lego man: front-right -> North-West.
Consistent with Lego man being approx (-3, 3) and Bike being (-5, 2)?
Red door is West. Say (-5, 0) or (-6, 0).

5. Jump to Red door.
- Jumped to Red door.
- Pos approx (-6, 0).
- Observe facing West.
- See into Room 2.
- Rubberduck: front-slight-right (W-NW). Sl. far. Facing right (North).
- Truck: front-right (NW). Mid dist. Facing backward (East).
- Lamp: front-right (NW). Sl. far.

6. Jump to Truck.
- Truck was mid-dist front-right from Red door.
Red door (-6, 0). Facing West. Front-Right is NW.
Truck approx (-6-2, 0+2) = (-8, 2)?
- At Truck facing West.
- Rubberduck: front (West), mid dist. Facing right (North).
- Lamp: front-right (NW), sl. far.

7. Rotate 90 (Face North) at Truck.
- Soda can: front (North), near.
- Lamp: front-left (NW), sl. far.
Truck (-8, 2). Soda can (-8, 3) or (-8, 4).
Lamp was NW from Truck? No, from Truck facing W, Lamp was Front-Right (NW).
From Truck facing N, Lamp is Front-Left (NW). Consistent.

8. Rotate 90 (Face East) at Truck.
- Red door: front-right (SE). Mid dist.
Truck (-8, 2). Red door (-6, 0).
Diff is (+2, -2). Facing East (+x). Front is +x. Right is -y.
Front-Right is (+x, -y). SE. Consistent.

9. Jump to Red door (approx -6, 0). Then to Green door.
- Green door was East, near.
- Initial pos (0,0). Green door (2,0).
- Jump to Green door. Pos (2,0).
- Observe.
Facing? I jumped from Red door (-6,0) to Green door (2,0). Movement is East. Orientation doesn't change during JumpTo?
Rules: "JumpTo(OBJ)... Your orientation does NOT change."
I was at Truck, facing South -> Rotated -90 -> East.
Jumped to Red door. Facing East.
Jumped to Green door. Facing East.
So I am at Green door facing East.
View into Room 3 (East of Green door).
- Toilet: front-slight-right (E-SE). Sl. far. Facing forward (East).
- Fridge: front-right (SE). Sl. far.
- Basket: front-slight-left (E-NE). Mid dist.

Coord estimation:
Room 1 (Center 0,0):
- Green door: (2, 0).
- Red door: (-6, 0) (Based on "sl. far" from origin? Origin->Red door: West. Sl far (4-8). Let's say -5 or -6).
- Lego man: NW. (-2, 2).
- Bike: Near Lego man, West of it. (-3, 2).
- Backpack: SW. (-2, -2).
- Shopping cart: SE. (2, -2).

Room 2 (West of Red door):
- Red door at (-6, 0).
- Truck: NW of door. (-8, 2).
- Soda can: North of Truck (near). (-8, 3).
- Rubberduck: West of Truck (mid). (-11, 2).
- Lamp: NW of Truck (sl far). (-10, 4)?

Room 3 (East of Green door):
- Green door at (2, 0).
- Facing East.
- Basket: E-NE (mid). (2+3, 0+1) = (5, 1).
- Toilet: E-SE (sl far). (2+5, 0-1) = (7, -1).
- Fridge: SE (sl far). (2+4, 0-3) = (6, -3).

Let's refine coordinates to be integers.
Agent is currently at Green door (2, 0). Facing East.

Object list:
- agent: [2, 0], facing: east
- lego man: [-2, 2], facing: south
- green door: [2, 0]
- backpack: [-2, -2], facing: south
- shoppingcart: [2, -2], facing: west
- bike: [-4, 2], facing: south
- red door: [-5, 0] (Let's set it at -5, "slightly far" 4-8. 5 fits).
- rubberduck: [-9, 2], facing: north (From truck [-7, 2] facing west, duck is front mid).
- truck: [-7, 2], facing: east (Back at truck, facing East, door was SE mid dist. Door -5,0. Truck -7,2. Diff +2,-2. Dist 2.8. Matches mid dist).
- lamp: [-9, 4] (From truck -7,2 facing N, lamp is Front-Left sl far. NW).
- soda can: [-7, 3] (From truck -7,2 facing N, soda is front near).
- toilet: [6, -1], facing: east (From Green door 2,0 facing E. Toilet is front-slight-right sl far. ~4 units East, 1 unit South? Dist 4.1. Fits sl far).
- fridge: [5, -3] (From Green door 2,0 facing E. Fridge is front-right sl far. SE).
- basket: [5, 1] (From Green door 2,0 facing E. Basket is front-slight-left mid. ~3 units E, 1 unit N).

Let's do a sanity check on "facing".
Lego man: "facing backward" when I looked North. So facing South.
Backpack: "facing forward" when I looked South. So facing South.
Shoppingcart: "facing right" when I looked South. So facing West.
Bike: "facing left" when I looked West. So facing South.
Truck: "facing backward" when I looked West (from red door). So facing East.
Rubberduck: "facing right" when I looked West (from red door). So facing North.
Toilet: "facing forward" when I looked East (from green door). So facing East.

Coordinates Summary:
Agent: [2, 0]
Lego man: [-2, 2]
Green door: [2, 0]
Backpack: [-2, -2]
Shoppingcart: [2, -2]
Bike: [-4, 2]
Red door: [-5, 0]
Truck: [-7, 2]
Rubberduck: [-10, 2]
Lamp: [-9, 4]
Soda can: [-7, 3]
Toilet: [7, -1]
Fridge: [6, -3]
Basket: [5, 1]

Justification for Green door at [2,0]: Observed "near" (0-2) from [0,0].
Justification for Red door at [-5,0]: Observed "slightly far" (4-8) from [0,0].

Refining relative positions:
Room 2:
Truck is "mid distance" from Red door [-5,0] facing West. Front-Right (NW).
Let's put Truck at [-7, 2]. Distance sqrt(2^2+2^2) = 2.8 (Mid is 2-4). OK.
Soda can is "near" Truck facing North. Front. [-7, 3]. Dist 1. OK.
Rubberduck is "mid distance" from Truck facing West. Front. [-10, 2]. Dist 3. OK.
Lamp is "slightly far" from Truck facing West. Front-Right (NW). [-10, 4]. Dist sqrt(3^2+2^2)=3.6 (Mid). Wait, observed "slightly far". Maybe [-11, 5]?
Let's stick to approximate.

Room 3:
From Green Door [2,0] facing East.
Basket: Front-slight-left (ENE). Mid (2-4). [5, 1]. Dist sqrt(3^2+1^2)=3.16. OK.
Toilet: Front-slight-right (ESE). Sl far (4-8). [7, -1]. Dist sqrt(5^2+1^2)=5.1. OK.
Fridge: Front-right (SE). Sl far (4-8). [5, -3]. Dist sqrt(3^2+3^2)=4.24. OK.

Final check on facings:
Lego man: South.
Backpack: South.
Shoppingcart: West.
Bike: South.
Truck: East.
Rubberduck: North.
Toilet: East.

The JSON should contain all these.

FINAL ANSWER:
```json
{
"agent": {"position": [2, 0], "facing": "east"},
"lego man": {"position": [-2, 2], "facing": "south"},
"green door": {"position": [2, 0]},
"backpack": {"position": [-2, -2], "facing": "south"},
"shoppingcart": {"position": [2, -2], "facing": "west"},
"bike": {"position": [-4, 2], "facing": "south"},
"red door": {"position": [-5, 0]},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-10, 2], "facing": "north"},
"lamp": {"position": [-10, 4]},
"soda can": {"position": [-7, 3]},
"toilet": {"position": [7, -1], "facing": "east"},
"fridge": {"position": [5, -3]},
"basket": {"position": [5, 1]}
}
```

THINK:
I need to construct the cognitive map based on my observations.
Initial state: Agent at (0,0) facing North in Room 1.
1. Observe at (0,0) facing N:
- Lego man: front-left, slightly far. Front-left is NW. Dist bins: near(0-2), mid(2-4), sl.far(4-8). "Slightly far" ~ 4-8.
Let's estimate...

{
  "agent": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "lego man": {
    "position": [
      -2,
      2
    ],
    "facing": "south"
  },
  "green door": {
    "position": [
      2,
      0
    ]
  },
  "backpack": {
    "position": [
      -2,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -2
    ],
    "facing": "west"
  },
  "bike": {
    "position": [
      -4,
      2
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -5,
      0
    ]
  },
  "truck": {
    "position": [
      -7,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -10,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -10,
      4
    ]
  },
  "soda can": {
    "position": [
      -7,
      3
    ]
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "fridge": {
    "position": [
      5,
      -3
    ]
  },
  "basket": {
    "position": [
      5,
      1
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  }
}

THINK:
I am currently at the green door. I previously established that I was facing East when I jumped to the green door. Since `JumpTo` does not change orientation, I am still facing East.
However, I need to check the orientation relative to the map.
Room 1 is the central room.
Red door is West. Green door is East.
I jumped from Red door (West side of Room 1) to Green door (East side of Room 1). My facing was East.
Now I am at the Green door, facing East.
I observe:
- Toilet: front-slight-right (relative to East facing, this is South-East). Slightly far.
- Fridge: front-right (South-East). Slightly far.
- Basket: front-slight-left (North-East). Mid distance.

The `Observe` output gives "front-slight-right", etc.
I need to produce a LOCAL cognitive map relative to the agent's current position and facing.
Agent is at origin (0,0) in local frame. +y is East (current facing).
+x is South (Right of East).
-x is North (Left of East).

Objects:
1. Toilet: "front-slight-right", "slightly far".
- "front-slight-right" is angle (0, 22.5]. Let's approximate.
- "slightly far" is (4, 8]. Let's say ~6.
- Angle ~11 deg right.
- x (local right) = 6 * sin(11) ~ 1.1
- y (local front) = 6 * cos(11) ~ 5.9
- Let's approximate integer coords. (1, 6) or (2, 5)?
- "Facing forward". My forward is East. So toilet faces East? Or faces "forward" relative to me? Usually "facing backward" means facing the agent. "facing forward" means facing away?
- The instruction says: "facing: ... ego ... or allo". The output format for observed objects usually specifies "facing backward", etc. This is egocentric.
- If I am facing East, and object faces "forward", it faces East. In local frame, that is +y.

2. Fridge: "front-right", "slightly far".
- "front-right" is (22.5, 45]. Let's say ~35 deg.
- Distance ~6.
- x ~ 6 * sin(35) ~ 3.4
- y ~ 6 * cos(35) ~ 4.9
- Coords (3, 5).
- No facing info provided? "facing" key is missing in observation string? "fridge: front-right, slightly far". Yes, no facing.

3. Basket: "front-slight-left", "mid distance".
- "front-slight-left" is [-22.5, 0). Let's say -11 deg.
- "mid distance" is (2, 4]. Let's say 3.
- x ~ 3 * sin(-11) ~ -0.6
- y ~ 3 * cos(-11) ~ 2.9
- Coords (-1, 3).
- No facing info.

Wait, the prompt asks for integer coordinates. I should make reasonable estimates.
Distance bins:
near: (0,2] -> 1-2
mid: (2,4] -> 3-4
slightly far: (4,8] -> 5-7

Basket (mid): dist ~3-4. Front-slight-left -> x slightly negative, y positive. (-1, 3) or (-1, 4).
Toilet (slightly far): dist ~5-7. Front-slight-right -> x slightly positive, y positive. (1, 5) or (2, 6).
Fridge (slightly far): dist ~5-7. Front-right -> x more positive. (3, 5) or (4, 4).

Let's pick:
Basket: [-1, 3]
Toilet: [1, 6]
Fridge: [4, 5]

Facings:
Toilet: "facing forward". Local +y.
Fridge: None.
Basket: None.

JSON Structure:
{
"origin": "agent",
"objects": {
"toilet": {"position": [1, 6], "facing": "+y"},
"fridge": {"position": [4, 5]},
"basket": {"position": [-1, 3]}
}
}

Let's refine coordinates based on bins.
Bins:
[-45, -22.5) -> front-left
[-22.5, 0) -> front-slight-left
(0, 22.5] -> front-slight-right
(22.5, 45] -> front-right

Basket: front-slight-left [-22.5, 0).
Position (-1, 3): angle atan(-1/3) = -18 deg. Fits.
Toilet: front-slight-right (0, 22.5].
Position (1, 6): angle atan(1/6) = 9.4 deg. Fits.
Fridge: front-right (22.5, 45].
Position (4, 5): angle atan(4/5) = 38 deg. Fits.

Looks consistent.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"toilet": {"position": [1, 6], "facing": "+y"},
"fridge": {"position": [4, 5]},
"basket": {"position": [-1, 3]}
}
}
```

THINK:
I am currently at the green door. I previously established that I was facing East when I jumped to the green door. Since `JumpTo` does not change orientation, I am still facing East.
However, I need to check the orientation relative to the map.
Room 1 is the central room.
Red door is West. Gr...

{
  "origin": "agent",
  "objects": {
    "toilet": {
      "position": [
        1,
        6
      ],
      "facing": "+y"
    },
    "fridge": {
      "position": [
        4,
        5
      ]
    },
    "basket": {
      "position": [
        -1,
        3
      ]
    }
  }
}

{
  "toilet": {
    "position": [
      1,
      5
    ],
    "facing": "east"
  },
  "fridge": {
    "position": [
      3,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      -1,
      3
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "toilet": {
      "position": [
        1,
        6
      ],
      "facing": "+y"
    },
    "fridge": {
      "position": [
        4,
        5
      ]
    },
    "basket": {
      "position": [
        -1,
        3
      ]
    }
  }
}

{
  "toilet": {
    "position": [
      1,
      5
    ],
    "facing": "east"
  },
  "fridge": {
    "position": [
      3,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      -1,
      3
    ],
    "facing": "east"
  }
}

THINK:
I am currently at the green door (marked as '*') which connects Room 1 (West of me) and Room 3 (East of me).
I am facing East into Room 3.
I have just observed:
- Toilet (front-slight-right)
- Fridge (front-right)
- Basket (front-slight-left)

My current position is at the doorway. I have vision into Room 3 (East). The area immediately in front of me (East) is observed.
The map shows Room 1 to the West (left), Room 2 to the far West (connected to Room 1), and Room 3 to the East (right).
Room 1 is the middle room on the map (where the + is).
Wait, let's look at the ASCII map.
The '*' is at the green door. To its left (West) is Room 1. To its right (East) is Room 3.
The map shows room structures.
Room 1: The room to the left of '*'.
Room 2: The room further left? The map shows `########......#......#`.
Wait, the map layout:
Left block: `......` (Room 2?)
Middle block: `......` (Room 1?)
Right block: `......` (Room 3?)
Doors: One '+' at (X,Y) approx between Left and Middle. And '*' is at the door between Middle and Right.
The ASCII map shows:
`#......+......*......#`
This implies 3 rooms horizontally.
Left room: connected by '+' to Middle room.
Middle room: connected by '*' to Right room.
My history:
Start in Room 1 (Middle).
Went to Red Door (West). Found Room 2 (Left).
Returned to Red Door.
Went to Green Door (East). Found Room 3 (Right).
So:
Left Room = Room 2.
Middle Room = Room 1.
Right Room = Room 3.

I am at '*', looking East into Room 3.
I have observed "front" (East), "front-right" (South-East), "front-left" (North-East).
My observation cone covers the area East of me.
Candidates A, B, C, D, E, F are in the Right Room (Room 3).
Points A, B, C, F seem to be in the upper/middle part of Room 3.
Points D, E are in the lower part of Room 3.
I am facing East.
Observed objects:
- Toilet: front-slight-right.
- Fridge: front-right.
- Basket: front-slight-left.
This means I have seen the cone towards East.
Let's check the coordinates of candidates relative to '*' (Door).
'*' is on the West wall of Room 3.
A: East and slightly South of center?
B: East and South of center.
C: East and North of center.
F: Far East and North?
D: South.
E: South West corner?

Wait, let's look at the map closely.
`#......+......*......#` row.
Below that row in Room 3:
`#C..F..#`
`#B...A.#`
`#.D....#`
`#E.....#`
This suggests Room 3 extends significantly South of the door '*'.
The door '*' is at the top-left of the visible part of Room 3 in this snippet?
No, the row with '*' is `......*......`.
Rows above it: `......`
Rows below it: `C..F..`, `B...A.`, `D....`, `E.....`
So the door is on the West wall, but towards the North end of the room?
Actually, the map shows `#` above the `*` row in that column? No, `*` is on a wall line.
Above `*` there is `#`?
Line above `*`: `#......#......#......#` (floor).
Wait, the wall line is vertical.
`#`
`#`
`*`
`#`
`#`
The ASCII map shows `*` is on the vertical divider.
Points A-F are in the space to the right of `*`.
The space extends South (down).
My view direction is East (Right).
My FOV is 90 degrees (+/- 45).
I see:
- Front (East): This covers the row of `*` and maybe slightly up/down.
- Front-Right (South-East): This covers the area `B`, `A`?
- Front-Left (North-East): This covers area above `*`?
Wait, the candidates are mostly South of the door row.
Row with `*`: Y_door.
C, F are in row Y_door - 1.
B, A are in row Y_door - 2.
D is in row Y_door - 3.
E is in row Y_door - 4.
If I face East:
- Right is South.
- Front-Right is South-East.
My FOV (East +/- 45) covers from North-East to South-East.
However, "Front-Right" (22.5 to 45 degrees right of East) corresponds to South-East.
Objects seen: Toilet (front-slight-right), Fridge (front-right).
These are in the South-East direction.
So I have likely seen B and A? Or at least the area.
What about C and F? They are in row Y-1. Relative to door (Y), they are slightly South. East is X+.
So they are East and slightly South. That is "Front-Slight-Right".
What about D? It is further South. More to the Right of my facing?
If I face East, South is 90 degrees Right.
FOV is only up to 45 degrees Right.
Points that are strictly South or South-South-East (angle > 45 deg) are NOT seen.
The door is at Y.
D is at Y-3. X seems to be X_door + 2 or 3.
Angle to D: atan(dy/dx) = atan(3/2) approx 56 degrees. This is > 45. So D is outside FOV.
E is at Y-4. X is X_door + 1?
Angle to E: atan(4/1) = 76 degrees. Outside FOV.
What about C and F?
C is Y-1. X+1. Angle 45 deg. Edge of FOV.
F is Y-1. X+4. Angle small. Inside FOV.
What about B? Y-2. X+1. Angle atan(2/1) = 63 deg. Outside FOV.
A? Y-2. X+5. Angle atan(2/5) = 21 deg. Inside FOV.

So:
Seen: A, F.
Maybe Seen: C (boundary).
Not Seen: B, D, E.
Wait, let's re-evaluate "Front-Right" bins.
(22.5, 45].
If angle is > 45, it is "Beyond FOV" (specifically "Right" but I don't see it).
So B (angle ~63) is unseen.
D (angle ~56) is unseen.
E (angle ~76) is unseen.
C (angle ~45) might be seen or not. 45 is the boundary.
F (angle ~14) is seen.
A (angle ~21) is seen.

Wait, looking at the ASCII carefully.
Row `*`: Y.
Row `C..F`: Y-1.
Row `B..A`: Y-2.
Row `D`: Y-3.
Row `E`: Y-4.

Let's estimate X coordinates relative to `*`.
`*` is at column X.
C is at X+1.
F is at X+4.
B is at X+1.
A is at X+5.
D is at X+2.
E is at X+0 or X+1? Looks like X+1.

Angles (Relative to East 0 deg, Clockwise +):
Vector to F: (+4, -1). Angle = atan(1/4) = 14 deg. (Front-Slight-Right). SEEN.
Vector to A: (+5, -2). Angle = atan(2/5) = 21.8 deg. (Front-Slight-Right). SEEN.
Vector to C: (+1, -1). Angle = atan(1/1) = 45 deg. (Front-Right boundary). Probably SEEN.
Vector to B: (+1, -2). Angle = atan(2/1) = 63.4 deg. > 45. NOT SEEN.
Vector to D: (+2, -3). Angle = atan(3/2) = 56.3 deg. > 45. NOT SEEN.
Vector to E: (+1, -4). Angle = atan(4/1) = 76 deg. > 45. NOT SEEN.

So Unexplored: B, D, E.
What about C? It's exactly on the edge. I'll count it as explored if I have to choose, or unexplored if I want to be safe. But B, D, E are definitely out.
Let's check the labels `toilet`, `fridge`, `basket`.
Toilet: front-slight-right (0 to 22.5). Matches F or A?
Fridge: front-right (22.5 to 45). Matches C? Or maybe A (21.8 is close to 22.5).
Basket: front-slight-left (0 to -22.5). This implies something North of the door. The map shows `#......#......#` above. There is space.

So, the area "South" of the view cone (Right side relative to agent) is unseen.
Candidates B, D, E are in that area.
Candidate C is on the edge.
Candidate A and F are likely seen.

Therefore, the unexplored points are B, D, E.
I should also check if C is considered unexplored. Usually, strictly 45 degrees is visible?
Let's stick to B, D, E as the clear ones.
Wait, is there anything North?
The map shows empty space `......` above `*`.
If `Basket` is front-slight-left, I saw something there.
So North-East is partially explored.

My selection: B, D, E.
Maybe C too?
Let's look at the example. `unexplored: ["A", "C"]`.
I will include B, D, E.
Is A and F explored?
F is at angle 14. Definitely in "front-slight-right".
A is at angle 21.8. In "front-slight-right".
C is at angle 45. "front-right".
So A, C, F are likely observed (or at least in the FOV).
B, D, E are outside the 45 degree cone.
So they are unexplored.

One more check: `fridge` is `front-right` (22.5-45). This matches C (45).
`toilet` is `front-slight-right` (0-22.5). Matches F (14) or A (21.8).
So objects were seen in the directions of F, A, C.
Thus A, C, F are explored.
B, D, E are not.

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

THINK:
I am currently at the green door (marked as '*') which connects Room 1 (West of me) and Room 3 (East of me).
I am facing East into Room 3.
I have just observed:
- Toilet (front-slight-right)
- Fridge (front-right)
- Basket (front-slight-left)

My current position is at the doorway. I have vis...

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

You jumped to green door. You observe:
• toilet: front-slight-right, slightly far, facing forward
• fridge: front-right, slightly far
• basket: front-slight-left, mid distance.
You have a maximum of 9 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to green door. You observe:
• toilet: front-slight-right, slightly far, facing forward
• fridge: front-right, slightly far
• basket: front-slight-left, mid distance.
You have a maximum of 9 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
F...

I am at the green door, facing East (into Room 3).
I see:
- Toilet (front-slight-right)
- Fridge (front-right)
- Basket (front-slight-left)
This is Room 3. I need to map it completely.
I should jump into the room to get a better view and scan 360 degrees.
The basket is "mid distance". The others are "slightly far".
I'll jump to the basket.
Then I'll observe.

I am at the green door, facing East (into Room 3).
I see:
- Toilet (front-slight-right)
- Fridge (front-right)
- Basket (front-slight-left)
This is Room 3. I need to map it completely.
I should jump into the room to get a better view and scan 360 degrees.
The basket is "mid distance". The others are...

THINK:
I need to construct the JSON map based on the observations so far.
Initial position: (0,0), facing North (Room 1).
Observations in Room 1:
1. **Pos (0,0), Facing North:**
* `lego man`: front-left, slightly far. (Front=N, Left=W -> NW).
2. **Pos (0,0), Facing East:**
* `green door`: front, near. (Front=E -> E). Dist ~2.
3. **Pos (0,0), Facing South:**
* `backpack`: front-right, mid. (Front=S, Right=W -> SW). Dist ~3-4.
* `shoppingcart`: front-left, mid. (Front=S, Left=E -> SE). Dist ~3-4.
* Relation: backpack is east, near shoppingcart. (Wait, previous line said backpack front-right (SW) and shoppingcart front-left (SE). That puts backpack West of Shoppingcart. But relation says "backpack is east... to shoppingcart". This is a contradiction or I misread "facing".
* Re-read South obs: "backpack: front-right... facing forward". "shoppingcart: front-left... facing right". "backpack is east, near to shoppingcart".
* If facing South: Front=South. Right=West. Left=East.
* Backpack at front-right -> South-West.
* Shoppingcart at front-left -> South-East.
* This puts Backpack WEST of Shoppingcart.
* The relation text says "backpack is east". This contradicts the ego-centric observation. I will trust the ego-centric observation coordinates more but double check. Maybe "front-right" meant "front and to the right"? Facing South, right is West.
* Let's check the text again: "backpack: front-right". "shoppingcart: front-left".
* Let's assume the relation text might have swapped them or used a different reference? Or maybe I'm swapped.
* Usually, relations are reliable. Let's look at the next obs.
4. **Pos (0,0), Facing West:**
* `bike`: front-slight-right, mid. (Front=W, Right=N -> WNW).
* `lego man`: front-right, slightly far. (Front=W, Right=N -> NW). Confirms Lego man is NW.
* `red door`: front, slightly far. (Front=W -> W). Dist ~5-6?
* Relation: "bike is west, near to lego man". Lego man is NW. Bike is W of it. So Bike is further West?

Let's estimate coordinates.
Room 1 (Origin 0,0):
* Agent starts at (0,0).
* `green door`: East, near. Let's say (2,0) or (0,2)? North is +y. East is +x. So Green Door ~ (2, 0).
* `red door`: West, slightly far. West is -x. Dist ~5. Say (-5, 0).
* `lego man`: NW. From (0,0), facing N, front-left. Facing W, front-right. Consistent. Coord approx (-3, 3).
* `bike`: WNW. West of Lego man. (-5, 3)?
* `backpack` & `shoppingcart`: South-ish. Backpack SW, Cart SE. Backpack (-2, -3), Cart (2, -3)? Relation says "backpack is east". This contradicts SW/SE placement (Backpack West, Cart East). I will assume the ego-centric labels "front-right" (West side when facing S) and "front-left" (East side when facing S) are correct, meaning Backpack is West and Cart is East. The relation "backpack is east" might mean "backpack is TO THE east OF shoppingcart"? No, "backpack is east, near to shoppingcart" usually means "backpack is located east relative to shoppingcart". This remains a conflict. I will stick to the ego-centric view: Backpack ~ (-2, -3), Cart ~ (2, -3).

Room 2 (Through Red Door at West):
* Jumped to `red door`. Facing West.
* Obs: `rubberduck` (front-slight-right -> W/NW), `truck` (front-right -> NW), `lamp` (front-right -> NW).
* Jumped to `truck`. Facing West.
* Obs: `rubberduck` (front -> West of truck), `lamp` (front-right -> NW of truck).
* Rotated to North (at truck): `soda can` (front -> N of truck), `lamp` (front-left -> NW of truck).
* Rotated to East (at truck): `red door` (front-right -> SE of truck).
* If Red Door is at (-5, 0) and is SE of Truck, then Truck is NW of Door.
* Truck coords: Red Door is (-5,0). Truck is NW. Let's say (-7, 2).
* Check Red Door obs from Truck (East facing): "front-right". Front=E, Right=S. So SE. Correct.
* `rubberduck`: West of Truck. (-9, 2).
* `soda can`: North of Truck. (-7, 4).
* `lamp`: NW of Truck. (-9, 4).
* Room 2 seems to be at the West end.

Room 3 (Through Green Door at East):
* Jumped to `green door` (at ~2,0). Facing East.
* Obs: `toilet` (front-slight-right -> E/SE), `fridge` (front-right -> SE), `basket` (front-slight-left -> E/NE).
* Jumped to `basket`. Facing East.
* Obs: `toilet` (front-right -> SE of basket).
* Green Door at (2,0). Basket is E/NE. Say (4, 1) or (5, 2).
* Toilet is SE of Basket. If Basket (5,2), Toilet (6, 0)?
* Fridge is SE from Door. (5, -2)?

Refining Coordinates:
Scale:
Near: 1-2. Mid: 3-4. Slightly far: 5-8.
Red Door (slightly far from 0,0 West): x = -5.
Green Door (near from 0,0 East): x = 2.
Truck (mid from Red Door? No, observed from door as mid).
From Red Door (-5,0), facing West:
Truck is front-right (NW). Dist mid (3-4).
dx ~ -2, dy ~ 2. Truck ~ (-7, 2).
From Truck (-7,2) facing East: Red Door is front-right (SE). Matches.
From Truck (-7,2) facing West: Rubberduck is front (W). Dist mid (3-4). Rubberduck ~ (-10, 2).
From Truck (-7,2) facing North: Soda can is front (N). Dist near (1-2). Soda can ~ (-7, 4).
Lamp is front-left (NW). Dist slightly far (5-8). Lamp ~ (-10, 5).

Green Door (2,0).
From Green Door facing East:
Basket is front-slight-left (ENE). Dist mid (3-4).
dx ~ 3, dy ~ 1. Basket ~ (5, 1).
From Basket (5,1) facing East:
Toilet is front-right (SE). Dist mid (3-4).
dx ~ 2, dy ~ -2. Toilet ~ (7, -1).
From Green Door: Toilet was front-slight-right (ESE). Dist slightly far (5-8).
(2,0) to (7,-1) is dx=5, dy=-1. Matches ESE and distance.
Fridge from Green Door: front-right (SE). Dist slightly far.
Maybe (5, -3).

Objects and Facings:
Agent: Currently at `basket`. Facing East.
Lego man: (-3, 3). Facing: West obs said "facing left" (South). North obs said "facing backward" (South). So South.
Green door: (2, 0).
Red door: (-5, 0).
Backpack: (-2, -3). Facing: South obs said "facing forward" (South).
Shoppingcart: (2, -3). Facing: South obs said "facing right" (West).
Bike: (-5, 3). Facing: West obs said "facing left" (South).
Truck: (-7, 2). Facing: From door (facing W), truck facing backward (East).
Rubberduck: (-10, 2). Facing: From door (facing W), facing right (North). From truck (facing W), facing right (North). So North.
Lamp: (-10, 5). No facing info observed? From door: "front-right". From truck: "front-left". No facing.
Soda can: (-7, 4). No facing.
Basket: (5, 1). No facing observed? "mid distance". No facing info.
Toilet: (7, -1). Facing: From basket (facing E), facing forward (East). From door (facing E), facing forward (East). So East.
Fridge: (5, -3). No facing.

Wait, I missed one relation check.
"backpack is east, near to shoppingcart".
My coords: Backpack (-2, -3), Cart (2, -3). Backpack is WEST.
If the relation is true, then Backpack is (2, -3) and Cart is (-2, -3).
Let's re-read the Observation from 0,0 Facing South.
"backpack: front-right" -> South-West.
"shoppingcart: front-left" -> South-East.
"backpack is east, near to shoppingcart".
This is a direct contradiction. "Front-right" is definitely Agent's right. If facing South, Right is West.
Maybe I should trust the Ego-centric relative to the Agent more than the processed "relation"? Or maybe "facing south" means something else?
Standard convention: Facing South. Forward=South (-y). Right=West (-x). Left=East (+x).
So Backpack is -x. Cart is +x. Backpack is West of Cart.
The relation says "backpack is east".
Possibility: The agent's facing was not South? No, "You rotated clockwise 90°" (from East) -> South.
Possibility: The relation description is relative to the object's frame? No, "backpack is east...".
Possibility: Error in problem statement. I will follow the explicit ego-centric observations (front-right/front-left) as they are the primary data. I will place Backpack West and Shoppingcart East.

Final check of list:
Room 1:
- Lego man
- Green door
- Red door
- Backpack
- Shoppingcart
- Bike
Room 2:
- Truck
- Rubberduck
- Lamp
- Soda can
Room 3:
- Basket
- Toilet
- Fridge

Agent is at Basket.

Steps so far:
1. Observe
2. Rotate(90), Observe
3. Rotate(90), Observe
4. Rotate(90), Observe
5. JumpTo(red door), Observe
6. JumpTo(truck), Observe
7. Rotate(90), Observe
8. Rotate(90), Observe
9. Rotate(90), Observe
10. Rotate(-90), JumpTo(red door), Observe
11. JumpTo(green door), Observe
12. JumpTo(basket), Observe

Total 12 steps used. 8 left.
I am at the basket. I have scanned Room 3 partially (Observed from Green Door, Observed from Basket).
From Basket (facing East), I saw Toilet (front-right).
From Green Door (facing East), I saw Toilet, Fridge, Basket.
I haven't seen "left" (North) or "back" (West) from the Basket fully.
The basket is at (5,1).
I should check the rest of Room 3.
I'll rotate 90 degrees (clockwise or counter) to scan the rest.
But first, I must output the JSON map.

JSON Map Construction:
Agent: [5, 1], facing: "east" (Assumed coords based on grid logic).
Let's try to integerize properly.
Origin (0,0).
Green Door: (2, 0).
Red Door: (-4, 0) or (-5, 0).
Lego man: (-2, 2).
Bike: (-4, 2).
Backpack: (-2, -3).
Shoppingcart: (2, -3).
Truck: (-6, 2).
Soda can: (-6, 4).
Lamp: (-8, 4).
Rubberduck: (-8, 2).
Basket: (5, 1).
Toilet: (6, -1).
Fridge: (5, -3).

Verify facing directions:
Lego man: "facing backward" (from North view) -> South.
Backpack: "facing forward" (from South view) -> South.
Shoppingcart: "facing right" (from South view) -> West.
Bike: "facing left" (from West view) -> South.
Truck: "facing backward" (from West view) -> East.
Rubberduck: "facing right" (from West view) -> North.
Toilet: "facing forward" (from East view) -> East.

I will use these for the JSON.

FINAL ANSWER:
```json
{
"agent": {"position": [5, 1], "facing": "east"},
"bike": {"position": [-4, 2], "facing": "south"},
"lego man": {"position": [-2, 2], "facing": "south"},
"red door": {"position": [-4, 0], "facing": "east"},
"green door": {"position": [2, 0], "facing": "west"},
"backpack": {"position": [-2, -3], "facing": "south"},
"shoppingcart": {"position": [2, -3], "facing": "west"},
"truck": {"position": [-6, 2], "facing": "east"},
"rubberduck": {"position": [-8, 2], "facing": "north"},
"lamp": {"position": [-8, 4]},
"soda can": {"position": [-6, 4]},
"basket": {"position": [5, 1]},
"toilet": {"position": [6, -1], "facing": "east"},
"fridge": {"position": [5, -3]}
}
```

THINK:
I need to construct the JSON map based on the observations so far.
Initial position: (0,0), facing North (Room 1).
Observations in Room 1:
1. **Pos (0,0), Facing North:**
* `lego man`: front-left, slightly far. (Front=N, Left=W -> NW).
2. **Pos (0,0), Facing East:**
* `green doo...

{
  "agent": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      -4,
      2
    ],
    "facing": "south"
  },
  "lego man": {
    "position": [
      -2,
      2
    ],
    "facing": "south"
  },
  "red door": {
    "position": [
      -4,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      -2,
      -3
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      2,
      -3
    ],
    "facing": "west"
  },
  "truck": {
    "position": [
      -6,
      2
    ],
    "facing": "east"
  },
  "rubberduck": {
    "position": [
      -8,
      2
    ],
    "facing": "north"
  },
  "lamp": {
    "position": [
      -8,
      4
    ]
  },
  "soda can": {
    "position": [
      -6,
      4
    ]
  },
  "basket": {
    "position": [
      5,
      1
    ]
  },
  "toilet": {
    "position": [
      6,
      -1
    ],
    "facing": "east"
  },
  "fridge": {
    "position": [
      5,
      -3
    ]
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  }
}

{
  "bike": {
    "position": [
      -3,
      1
    ],
    "facing": "south"
  },
  "airplane": {
    "position": [
      3,
      -3
    ],
    "facing": "south"
  },
  "rubberduck": {
    "position": [
      -11,
      1
    ],
    "facing": "north"
  },
  "lego man": {
    "position": [
      -3,
      3
    ],
    "facing": "south"
  },
  "toilet": {
    "position": [
      7,
      -1
    ],
    "facing": "east"
  },
  "truck": {
    "position": [
      -7,
      1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -1,
      -2
    ],
    "facing": "south"
  },
  "shoppingcart": {
    "position": [
      1,
      -2
    ],
    "facing": "west"
  },
  "fridge": {
    "position": [
      5,
      -3
    ],
    "facing": "east"
  },
  "soda can": {
    "position": [
      -7,
      3
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  },
  "lamp": {
    "position": [
      -11,
      5
    ],
    "facing": "east"
  },
  "red door": {
    "position": [
      -5,
      0
    ],
    "facing": "east"
  },
  "green door": {
    "position": [
      2,
      0
    ],
    "facing": "east"
  },
  "agent": {
    "position": [
      5,
      1
    ],
    "facing": "east"
  }
}

THINK:
I am at the basket in Room 3.
I faced East to enter the room. I jumped to the basket. Orientation is still East.
So my "forward" (+y) is East (Global).
My "right" (+x) is South (Global).
My "left" (-x) is North (Global).
My "backward" (-y) is West (Global).

I see:
- toilet: front-right, mid distance.
- "front-right" means in the (+x, +y) quadrant.
- "mid distance" means (2, 4]. Let's estimate distance ~3.
- Angle ~45 degrees?
- Coords: x ~ +2, y ~ +2 ? Or x ~ +2, y ~ +1.
- Object facing: "facing forward". My forward is East. So object faces East. Relative to me (East), East is +y.

JSON format:
origin: agent
objects:
toilet: position relative to agent.
facing relative to agent's frame.

Let's refine coordinates.
Toilet is front-right. Mid distance.
Let's guess [2, 2] or similar.
Facing: "facing forward". Since agent faces East, "forward" means East.
In local frame, East is +y. So facing is "+y".

Only the toilet is mentioned in the last observation.

Wait, in the previous observation from the door (facing East):
- Basket was front-slight-left, mid distance.
- Toilet was front-slight-right, slightly far.
- Fridge was front-right, slightly far.

Now I am at the basket.
I see the toilet to the front-right, mid distance.
The fridge was not reported in the latest observation? Maybe it's out of FOV now? Or blocked?
The latest observation only lists "toilet".
So I only include "toilet".

Local Map:
Agent is at (0,0) facing +y.
Toilet: front-right -> +x, +y.
Distance: mid (2-4).
Let's say x=2, y=2.
Facing: "facing forward" -> faces the same way I am facing?
"facing forward" usually means facing the agent?
Wait, "facing backward" means facing away from agent?
Let's check the definitions.
"forward/backward/right/left (ego) ... When agent faces north: forward = north".
Usually "facing forward" means the object's front is pointing in the direction 'forward'.
If I am facing North, and object is facing forward (North), its front points North.
Here I am facing East. Object is facing forward (East).
So in local frame (where +y is East), object faces +y.

Positions:
Toilet at [2, 2]?
Let's check bins.
Angle bins: front-right is (22.5, 45].
Mid distance is (2, 4].
If x=1, y=3 -> angle atan(1/3) ~ 18 deg (front-slight-right).
If x=2, y=2 -> angle 45 deg (front-right).
If x=3, y=1 -> angle ~71 deg (right, not front-right).
So [2, 2] is a good guess for front-right.
Or [1, 2]? atan(0.5) = 26 deg. This is in front-right (22.5, 45].
Or [2, 3]? atan(0.66) = 33 deg.
Distance: sqrt(1^2 + 2^2) = 2.23 (mid).
sqrt(2^2 + 2^2) = 2.82 (mid).
sqrt(2^2 + 3^2) = 3.6 (mid).
Let's pick [2, 3] as a representative position for "mid distance, front-right". Or [2, 2].
Let's go with [2, 2].

Facing:
"facing forward".
Agent faces East. Object faces East.
Local frame: East is +y. Object faces +y.

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"toilet": {"position": [2, 2], "facing": "+y"}
}
}

THINK:
I am at the basket in Room 3.
I faced East to enter the room. I jumped to the basket. Orientation is still East.
So my "forward" (+y) is East (Global).
My "right" (+x) is South (Global).
My "left" (-x) is North (Global).
My "backward" (-y) is West (Global).

I see:
- toilet: front-right, mid ...

{
  "origin": "agent",
  "objects": {
    "toilet": {
      "position": [
        2,
        2
      ],
      "facing": "+y"
    }
  }
}

{
  "toilet": {
    "position": [
      2,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "toilet": {
      "position": [
        2,
        2
      ],
      "facing": "+y"
    }
  }
}

THINK:
I am currently at the basket (marked as * on the map) in Room 3 (the rightmost room). My current orientation is East (inherited from the jump).
I have observed:
- From green door (facing East): Toilet (front-slight-right), Fridge (front-right), Basket (front-slight-left).
- From basket (facing East): Toilet (front-right).
This implies the Toilet is generally East/South-East of the basket.
Looking at the map:
Room 1 is the middle one (connected to left and right).
Room 2 is on the left (West).
Room 3 is on the right (East).
I am at the basket in Room 3.
The map shows candidate points A, B, C, D, E, F within Room 3.
B is near the agent (Basket).
F is East of the door, near the middle.
C, D, E, A are in the lower (South) part of Room 3.
I have only looked East from the Green Door and East from the Basket.
My East view from the basket (facing East) covers the area to the East of the basket.
The toilet was seen front-right from the basket. If facing East, front-right is South-East. So I have seen somewhat towards C.
However, I have not looked South, West, or North from the basket.
The points A, C, D, E are in the South part of the room.
I have barely seen the South part (only via "front-right" peripheral).
Points A, D, E are likely unobserved or poorly observed. C might be the toilet or near it? No, toilet is an object.
"Select the points that are located in unexplored/unobserved regions."
I have not scanned North, South, or West from the basket.
The map shows:
B is very close to *. It's likely observed or is the location itself.
F is between the door and the basket. I jumped over it? Or it's the space I traversed.
A, C, D, E are in the southern area. I haven't turned South yet.
My observations:
From Door (looking East): Saw "Toilet: front-slight-right", "Fridge: front-right". This covers the vector towards South-East.
From Basket (looking East): Saw "Toilet: front-right".
The area directly South (A, D, E) and the far South-East corner (C) might be unobserved or only partially observed.
Specifically, if I look East, my FOV is [-45, 45].
Anything strictly South (e.g. -90 deg relative to East) is not seen.
Points A, D, E seem to be in the South / South-West direction from the basket.
Point C is South-East.
Given I haven't rotated, I haven't seen the walls or corners to my North, South, or West (back at the door).
Unexplored regions are definitely the South part (A, D, E, maybe C) and North part (above B).
Candidates listed: A, B, C, D, E, F.
B is right next to me.
F is in the path from the door.
A, C, D, E are in the deep south of the room.
I haven't looked South.
So A, C, D, E are unexplored.
Wait, I saw "Toilet" to the front-right. That is South-East. C looks like it's in the South-East corner. It might be near the toilet.
However, "unexplored/unobserved" usually implies areas not covered by the FOV cones of previous observations.
My FOV from the door covered the cone East.
My FOV from the basket covered the cone East.
The region South of the basket (90 deg clockwise) has NOT been observed.
The region North of the basket has NOT been observed.
The region West (backwards) has NOT been observed from this position (though seen from the door).
On the map:
A is South.
C is South-East.
D is South-West (relative to basket? No, D is directly South of the door roughly, E is further West?).
Let's look at the ASCII carefully.
Basket (*) is at roughly x=18, y=6 (counting from bottom left 0,0 approx).
Room 3 seems to be x=14 to 21.
Green door (+) at x=14, y=6.
Agent (*) at x=19, y=6.
B is at x=18, y=6 (left of Agent).
F is at x=17, y=6.
D is x=16, y=3?
E is x=15, y=3?
A is x=17, y=2?
C is x=20, y=3?
My observations:
1. At Door (14,6) facing East:
- Basket at (19,6)? "front-slight-left"? No, if I am at (14,6) and Basket is at (19,6), that is straight East (0 deg).
- "Basket: front-slight-left". This implies Basket is slightly North of East? Or my facing wasn't perfect East? I faced East.
- If Basket is front-slight-left, maybe it's at (19, 7)?
- "Toilet: front-slight-right". South of East.
- "Fridge: front-right". More South.
2. At Basket (*) facing East:
- "Toilet: front-right".
- This confirms Toilet is South-East of Basket.
- So the cone East from Basket covers (East, South-East).
- The area directly South (A, D, E) is likely missed.
- Area C (South-East) might be in the "front-right" FOV, but maybe not fully resolved or "unexplored" in terms of walking there?
- Usually "unexplored" means not seen.
- I have definitely NOT seen A, D, E.
- C is in the direction of the Toilet. I've seen the Toilet. Is C the Toilet? Maybe.
- B is "Near".
- F is "Near".
- The question asks for points in "unexplored/unobserved regions".
- I haven't looked North. Is there a point there? No.
- I haven't looked South. Points A, C, D, E are South.
- I haven't looked West.
- The points A, D, E are definitely out of the East-facing FOV from the basket (which is 45 deg right -> SE).
- A is almost directly South.
- D, E are South-West.
- C is South-East. It might be seen.
- However, without looking South, I can't be sure of the layout there.
- I'll select A, C, D, E as they are in the unvisited/unobserved southern lobe. B and F are on the path I just took or very close.

Refining:
- F is West of me. I came from West. I saw it from the door.
- B is West of me (between me and F). Saw it from door.
- C is South-East. Saw "Toilet" there. But ground might be unobserved?
- A, D, E are South/South-West. I faced East. FOV is +/- 45 deg.
- South is -90 deg. Definitely not seen from Basket.
- From Door (facing East), D and E are South-East?
- Door at (14,6). D at (16,3). Vector (2, -3). Angle approx -56 deg.
- FOV is +/- 45 deg.
- -56 is outside [-45, 45].
- So D and E were NOT seen from the door either.
- A at (17,2). Vector (3, -4). Angle -53 deg. Not seen.
- C at (20,3). Vector (6, -3). Angle -26 deg. This IS in FOV [-45, 45].
- So C was likely seen (or the area was).
- But A, D, E were likely NOT seen.

Wait, earlier I saw "Toilet: front-slight-right" from Door.
- "front-slight-right" is [0, 22.5].
- "front-right" is [22.5, 45].
- If Toilet is at C (angle -26 deg), it would be "front-right".
- If Fridge is "front-right".
- Is there anything further South?
- A, D, E are lower (more South) than C? No, C is y=3, A is y=2.
- A is definitely not seen.
- D, E are definitely not seen.
- C is borderline, but likely seen if Fridge/Toilet are there.
- However, safest bet for "unexplored" is the ones definitely outside FOV.
- A, D, E.
- What about C? If it's the corner, maybe I need to check it.
- But strictly "unobserved": A, D, E.
- I will include C just in case, or stick to the obvious ones. The prompt asks for "unexplored/unobserved". A, D, E are definitely unobserved. C is likely observed (contains objects).
- Let's check the map again. C is near the wall.
- I'll select A, C, D, E to be safe, or just A, D, E?
- C is at (20,3). Basket at (19,6). Vector (1, -3). Angle -71 deg relative to East.
- From Basket facing East, C is -71 deg. "Front-right" is usually up to 45 deg.
- So C is NOT seen from Basket facing East.
- Was C seen from Door? Door (14,6) to C (20,3). Vector (6, -3). Angle -26.5 deg.
- Yes, seen from Door.
- But is it "Explored"? Exploring usually means visiting or seeing clearly.
- Maybe I'll stick to A, D, E.
- Wait, map shows A, C, D, E in a cluster.
- Let's assume the question implies "which points should I go to / haven't seen well".
- I'll pick A, C, D, E.

Actually, looking closer at C from Basket:
Angle is -71 deg. This is outside FOV.
From Door, it was visible.
However, usually these fog maps track *cumulative* coverage?
If I saw it from the door, it's observed.
But A, D, E were NOT seen from door (angles < -45).
So A, D, E are definitely unobserved.
C was likely seen from the door.
So "unexplored" = A, D, E.

Let's re-verify D and E from Door.
Door (14,6). E (15,3). Vector (1, -3). Angle -71. Not seen.
D (16,3). Vector (2, -3). Angle -56. Not seen.
A (17,2). Vector (3, -4). Angle -53. Not seen.
So A, D, E are definitely unobserved.
C (20,3). Vector (6, -3). Angle -26. Seen.
So C is observed.

Therefore, unobserved: A, D, E.

One catch: "front-right" usually means [22.5, 45].
If an object was at -50 deg, it would be "beyond-fov".
Since I saw "Fridge: front-right", the fridge is in [22.5, 45] (clockwise positive? No, 0 is front. Right is +).
Wait, bearing definitions:
"Bearing is a degree in [-180, 180]; 0° is front. +: clockwise".
So Right is +90.
"front-right" is (22.5, 45].
So objects in +22.5 to +45 degrees.
This corresponds to South-East (if facing East).
My calculations:
C from Door: dx=6, dy=-3. South-East.
In standard math (East=0, North=90), SE is -45.
In Agent frame (Front=0):
Facing East. Object at SE.
Relative bearing is +45 approx.
So C is likely in "front-right".
A, D, E are "more South" than SE?
E: dx=1, dy=-3. This is almost South. Bearing approx +70 deg.
D: dx=2, dy=-3. Bearing approx +56 deg.
A: dx=3, dy=-4. Bearing approx +53 deg.
"front-right" max is 45 deg.
Anything > 45 is "right" or "back-right" or "beyond-fov"?
Bins: "otherwise -> beyond-fov"?
The bins listed are:
[-45,-22.5) FL
[-22.5,0) FSL
0 Front
(0,22.5] FSR
(22.5,45] FR
"otherwise -> beyond-fov".
So anything outside [-45, 45] is NOT reported in Egocentric bins.
This is a crucial rule!
So, if A, D, E have bearings > 45 deg, they are NOT seen.
E (approx 70) -> Not seen.
D (approx 56) -> Not seen.
A (approx 53) -> Not seen.
C (approx 26) -> Seen (in 22.5-45 bin).
So C is observed.
A, D, E are unobserved.

What about F and B?
F is (17,6). Door is (14,6). Bearing 0. Seen.
B is (18,6). Bearing 0. Seen.

So final answer should be A, D, E.

Wait, looking at the map again.
E is at x=15, y=3?
Map:
...
#......#......########
#......#......#.B*...# (y=6)
#......+......+..F...# (y=5) ?
########......#......# (y=4)
########......#......# (y=3)
###############ED..C.# (y=2)
###############..A...# (y=1)
###################### (y=0)

Let's count carefully.
Bottom wall is y=0.
Line above is y=1: "###############..A...#"
Line y=2: "###############ED..C.#"
Line y=3: "########......#......#"
Line y=4: "########......#......#"
Line y=5: "#......+......+..F...#" (This has the doors)
Line y=6: "#......#......#.B*...#" (Agent is here)
Line y=7: "#......#......########"

Agent is at y=6.
Door is at y=5.
Wait, "When you are at a door...". Door connects rooms.
Usually doors are in walls.
Line y=5 has "+......+".
So the wall is at y=5.
The agent is at y=6 (North of the wall)?
But "Room 1... Room 2... Room 3".
If I started in Room 1 facing North.
Room 1 is the middle one.
I went West to Room 2 (Left).
I came back.
I went East to Room 3 (Right).
Room 3 is the rightmost region.
Agent is in Room 3.
If the map coordinates have North as Up.
Room 3 layout:
Wall at Left (x=14?).
Wall at Bottom?
The ASCII map shows:
y=5: "#......+......+..F...#"
This looks like Room 1 is in the middle, Room 2 Left, Room 3 Right.
Doors are on the vertical walls separating rooms?
"Rooms connect via doors on vertical (front/back) or horizontal (left/right) walls."
Here the walls with doors seem to be vertical segments if the rooms are left/right.
ASCII:
Row y=5:
# (wall)
...... (Room 2 space)
+ (Red Door?)
...... (Room 1 space)
+ (Green Door?)
..F... (Room 3 space)
# (wall)

This implies the rooms are arranged Horizontally (East-West).
The doors are on vertical walls (x-constant).
Wait, the ASCII uses '+' for door.
If the layout is:
[Room 2] + [Room 1] + [Room 3]
Then the walls separating them are vertical lines.
The ASCII row y=5 shows the cross section?
But the rows above and below show walls '#' in the separation columns?
Row y=6: "#......#......#.B*...#"
Here '#' is at column 7 and 14?
So Room 2 is x=1..6.
Wall at x=7.
Room 1 is x=8..13.
Wall at x=14.
Room 3 is x=15..21.

Doors are at x=7 and x=14?
In row y=5, there is '+' at these spots.
So doors are at (7,5) and (14,5)?
Agent is at '*' in Room 3.
According to row y=6, Agent is at approx x=19.
Previous text said "green door... on front wall" when facing East in Room 1.
Front wall (East) of Room 1 is x=14. Correct.
I jumped to Green Door (14,5).
Then jumped to Basket.
Agent is now at '*' (x=19, y=6).

Candidates:
F is in row y=5, x=17?
B is in row y=6, x=18?
C is in row y=2, x=20?
D is in row y=2, x=17?
E is in row y=2, x=16?
A is in row y=1, x=18?

Check Visibility from Door (14,5) facing East (Direction = (1,0)):
- FOV [-45, 45].
- F (17,5): dx=3, dy=0. Angle 0. Seen.
- B (18,6): dx=4, dy=1. Angle +14. Seen.
- Agent (19,6): Seen.
- C (20,2): dx=6, dy=-3. Angle -26.5. Seen.
- D (17,2): dx=3, dy=-3. Angle -45. Borderline. (Bins: [-45, -22.5) is Front-Left. -45 is included? [-45... means yes).
- So D might be seen.
- E (16,2): dx=2, dy=-3. Angle -56. Not seen.
- A (18,1): dx=4, dy=-4. Angle -45. Borderline.

Check Visibility from Basket (19,6) facing East (Direction = (1,0)):
- FOV [-45, 45].
- C (20,2): dx=1, dy=-4. Angle -76. Not seen.
- D (17,2): dx=-2, dy=-4. Behind. Not seen.
- E (16,2): Behind. Not seen.
- A (18,1): dx=-1, dy=-5. Behind. Not seen.

So from Basket, none of A, C, D, E are seen.
From Door, C was seen. D and A are borderline -45. E was not seen.
"Unexplored" usually implies "I need to go there to see it".
If D and A are at -45 degrees, they are at the very edge.
Usually, fog maps highlight what has NOT been "cleared".
Given E is definitely not seen, and A/D are edge/far, and C is not seen from current pos (and might need closer look), I'd group the southern cluster.
However, if C was seen from the door, it might be cleared.
But E was definitely not.
A and D are edge cases.
If I have to choose, I will select the ones in the "shadow".
The shadow from Door (14,5) cast by the limit of FOV (-45 deg):
Line y = - (x-14) + 5 = -x + 19.
Points (x,y):
C (20,2): 2 vs -20+19=-1. 2 > -1. Inside FOV. (Cleared).
D (17,2): 2 vs -17+19=2. 2 = 2. On the line. (Cleared?).
A (18,1): 1 vs -18+19=1. 1 = 1. On the line. (Cleared?).
E (16,2): 2 vs -16+19=3. 2 < 3. Outside FOV. (Not Cleared).

So E is definitely unexplored.
A and D are on the boundary.
C is explored.
However, usually "Explore" task implies seeing all objects.
I saw "Toilet" and "Fridge" and "Basket".
Toilet was "front-slight-right" from Door? No, "front-slight-right" is [0, 22.5]?
Wait.
My observation from Door: "toilet: front-slight-right".
This means bearing in (0, 22.5].
My calculation for C (20,2) was angle -26.5 (Right is +? No, usually Left -, Right +).
Bearing definition: "+: clockwise".
So Right is Positive.
If C is at y=2 (South of y=5), that is to the Right when facing East.
So Bearing is positive.
Door (14,5), C (20,2). Vector (6, -3).
If Facing East (1,0).
Rotation clockwise to (6,-3)?
(1,0) -> (0,-1) is +90.
(6,-3) is roughly +26.5 deg.
So C is at +26.5 deg.
Bin: (22.5, 45] is "front-right".
Observation said "toilet: front-slight-right".
"front-slight-right" is (0, 22.5].
So the Toilet is NOT at C.
Toilet is at angle <= 22.5.
Maybe Toilet is at (20, 3) or (20, 4)?
If Toilet is at (20, 4): dx=6, dy=-1. Angle +9.5. This fits "front-slight-right".
So Toilet is North of C?
If C is at (20,2), it was NOT the Toilet.
Was C seen?
If C is at +26.5 deg.
Observation: "Fridge: front-right".
"front-right" is (22.5, 45].
So Fridge could be at C (20,2).
If Fridge is at C, then C is observed.

What about D, E, A?
D (17,2): dx=3, dy=-3. Angle +45.
Bin: (22.5, 45].
So D is "front-right".
Did I see anything else "front-right"?
Only "fridge".
If Fridge is at C, D might be empty space? Or unobserved?
If D is at 45 deg, it's inside FOV.
A (18,1): dx=4, dy=-4. Angle +45. Inside FOV.
E (16,2): dx=2, dy=-3. Angle +56. Outside FOV (>45).
So E is definitely Unobserved.

What about A and D?
They are at 45 deg. That is the limit.
Also, distance/occlusion?
If I saw Fridge at C, and D is closer?
Maybe D is empty.
But E is definitely hidden.
And looking at the cluster A, C, D, E.
Usually in these problems, the "corners" not visited are targets.
The Southern area (y=1, y=2) is largely unvisited.
I'm at y=6.
I've seen down to angle 45.
E is at angle 56.
A is at angle 45.
D is at angle 45.
I'll mark A, D, E as unexplored.
C is likely the Fridge (seen).
B, F are on the path.
So answer: A, D, E.

Wait, check coordinates of A again.
A is (18,1).
From Door (14,5): dx=4, dy=-4. Angle +45.
From Basket (19,6): dx=-1, dy=-5. Angle +101 (approx). Behind.
So A was at the limit of FOV from Door.
Usually "limit" implies might be missed or partially seen.
I will select A, D, E.

Final check on C.
If Fridge is at C, C is observed.
If C is empty space, it was in FOV.
So I will exclude C.

Result: A, D, E.

Wait, looking at the map again.
A is centered in the bottom alcove.
E and D are to the left of it.
The "alcove" y=1,2 is the main unobserved area.
I will select A, C, D, E to be sure?
No, C is likely seen.
Let's stick to A, D, E.
Actually, C is (20,2). Fridge at (20,2)?
If so, C is observed.
A (18,1) is deeper.
D (17,2) is West of C.
E (16,2) is West of D.
E is definitely hidden.
I'll go with A, D, E.

One more thought: The agent is at *, facing East.
He sees East.
The south part is to his Right.
He hasn't looked Right.
He hasn't looked South-West (E).
He hasn't looked South (D, A).
He hasn't looked South-East (C) *from this position*.
But he saw C from the door.
However, does the "Fog Probe" depend on global memory or current state? "Select the points that are located in unexplored/unobserved regions." implies global knowledge (map building).
Since C was seen from the door, it's observed.
E was NOT seen from the door.
A and D were at the limit.
I'll guess E is the most critical, A and D likely too.
Let's output A, D, E.

Wait, looking at the provided solution format example.
It's a JSON list.
I should be inclusive if unsure. A, C, D, E covers the whole southern strip.
If I miss one, it's bad. If I include a "seen" one, maybe less bad?
But "unobserved" is the criterion.
C is likely observed.
I will exclude C.
Final set: A, D, E.
Wait, let's look at B.
B is at (18,6). Next to agent (19,6).
From Door (14,5), B is at (18,6). dx=4, dy=1. Angle -14.
Seen from Door?
Facing East (0).
(4,1) is Left (Counter-Clockwise). Angle -14.
Bin: [-22.5, 0) "front-slight-left".
Observation from Door: "Basket: front-slight-left".
So B is the Basket?
"Basket: front-slight-left, mid distance".
Distance 4 roughly. (4 is "slightly far" or "mid"? (2,4] is mid, (4,8] is slightly far).
Distance sqrt(17) = 4.12 -> slightly far.
But observation said "mid distance".
Maybe Basket is at (17,6)? (F).
If Basket is at F (17,6): dx=3, dy=1. Dist 3.16 (Mid). Angle -18 (Front-slight-left).
This matches perfectly!
So Basket is at F.
If Agent jumped to Basket, Agent is at F?
But map shows Agent * at (19,6) and F at (17,6).
Prompt says "You jumped to basket."
So Agent is at Basket.
Map shows * at (19,6). So Basket is at (19,6).
Why did observation say "front-slight-left, mid distance" from Door?
Door (14,5) to (19,6). dx=5, dy=1. Dist 5.1 (Slightly Far). Angle -11.
Observation: "Basket: front-slight-left, mid distance".
Contradiction in distance? "mid distance" is (2,4]. 5.1 is > 4.
Maybe Door is at (15,5)?
If Door (15,5) to (19,6): dx=4, dy=1. Dist 4.12. Still > 4.
Maybe Basket is at (18,6) (B)?
Door (14,5) to (18,6): dx=4, dy=1. Dist 4.12.
Maybe (2,4] is strictly <= 4.
Maybe grid coordinates are different.
Anyway, B is likely the spot I passed or close.
The southern area A, D, E is definitely the unobserved one.
C is likely the Fridge.
So A, D, E.

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

THINK:
I am currently at the basket (marked as * on the map) in Room 3 (the rightmost room). My current orientation is East (inherited from the jump).
I have observed:
- From green door (facing East): Toilet (front-slight-right), Fridge (front-right), Basket (front-slight-left).
- From basket (facin...

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

You jumped to basket. You observe:
• toilet: front-right, mid distance, facing forward.
You have a maximum of 8 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to basket. You observe:
• toilet: front-right, mid distance, facing forward.
You have a maximum of 8 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am at the basket in Room 3, facing East.
I see the toilet.
I missed the fridge (maybe it's out of FOV or blocked?). It was "front-right" from the door.
I need to scan the room.
I will rotate 90 degrees clockwise to face South.

I am at the basket in Room 3, facing East.
I see the toilet.
I missed the fridge (maybe it's out of FOV or blocked?). It was "front-right" from the door.
I need to scan the room.
I will rotate 90 degrees clockwise to face South....

THINK:
I need to construct the cognitive map based on all observations.
Initial state: Agent at (0,0) facing North.

**Step 1: Room 1 (Initial)**
- Agent starts at (0,0), North.
- Observe() (North): Lego man front-left, slightly far.
- Rotate(90) -> East. Observe(): Green door front, near.
- "Near" is (0,2]. Let's say d=2.
- Green door at (2, 0) or (1, 0)? "Near" usually 1-2 units.
- Facing East, front is +x. So green door is at roughly (2, 0).
- Rotate(90) -> South. Observe(): Backpack front-right (SW), Shopping cart front-left (SE). Both mid distance (2-4).
- Facing South is -y.
- Backpack front-right relative to South -> West/South-West?
- Ego front-right is (22.5, 45]. South is 180. 180 + 30 = 210 (SW).
- Shopping cart front-left relative to South -> East/South-East? 180 - 30 = 150 (SE).
- Relation: Backpack is East, near Shopping cart?
- Wait, previous log said: "backpack: front-right... shoppingcart: front-left... backpack is east, near to shoppingcart."
- Facing South. Front-Right is Agent's West? No. Agent facing South. Right is West. Front-Right is South-West.
- Front-Left is South-East.
- If Backpack is SW and Cart is SE, then Backpack is West of Cart.
- But relation says "backpack is east, near to shoppingcart". This contradicts "Backpack SW, Cart SE".
- Let's re-read carefully. "backpack: front-right... shoppingcart: front-left". Facing South.
- Right of South is West. Left of South is East.
- So Backpack is SW. Cart is SE.
- Relation: "backpack is east, near to shoppingcart".
- Could the "facing direction called north" relative frame mean something else?
- "Use cardinal directions... Assume your current facing direction is called 'north'".
- If current facing (South) is "North", then "East" is Agent's Right (True West).
- So "Backpack is East (relative)" means Backpack is True West.
- This matches Backpack being Front-Right (True SW).
- So Backpack is West of Shopping Cart.
- Coordinates estimate:
- Agent (0,0).
- Backpack (SW, mid): (-2, -3)?
- Cart (SE, mid): (2, -3)?
- Rotate(90) -> West. Observe(): Bike front-slight-right, Lego man front-right, Red door front.
- Facing West (-x).
- Red door: Front (West), slightly far (4-8). Let's say x=-5.
- Lego man: Front-right (NW). Previously seen front-left from North (NW). Consistent.
- Bike: Front-slight-right (WNW).
- Relation: "bike is west, near to lego man". (Relative West = True North? No. Facing West = 'North'. West relative to 'North' is Left = True South? Or relative to global?)
- The relative relation text: "Assume your current facing direction is called 'north'".
- Current facing = West.
- "bike is west". West of 'North'(West) is 'West'(South)? Left is West.
- So Bike is Left of Lego man?
- Ego: Bike front-slight-right (slightly right of center). Lego man front-right (more right).
- So Lego man is more North than Bike.
- This implies Bike is South of Lego man.
- "Bike is west" relative to local frame? If local North is West, local West is South. Matches.
- Coordinates:
- Red door: (-5, 0).
- Lego man: (-4, 2)?
- Bike: (-4, 1)?

**Step 2: Room 2**
- JumpTo(Red door) -> Agent at (-5, 0). Facing West.
- JumpTo(Truck) -> Truck mid-distance front-right (NW relative to door, so W+N).
- Door at (-5,0). Facing West.
- Truck is NW. Distance ~3.
- Truck pos: (-7, 2)?
- From Truck (facing West, then North, then East, then South):
- Rubberduck: Front (West) from Truck.
- Lamp: Front-Right (NW) from Truck.
- Soda can: Front (North) from Truck.
- Red door: Front-Right (SE) from Truck when facing East.
- Truck at (-7, 2). Facing East. Front-Right is SE. Door at (-5, 0).
- dx = 2, dy = -2. Distance sqrt(8) ~ 2.8. Mid-distance (2-4). Matches.
- So Truck is definitely around (-7, 2).
- Soda can: Near North of Truck. (-7, 3).
- Rubberduck: West of Truck. (-9, 2).
- Lamp: NW of Truck. (-9, 4)?
- Observation from Door (looking West):
- Duck (front-slight-right) -> WNW.
- Truck (front-right) -> NW.
- Lamp (front-right) -> NW.
- Consistent.

**Step 3: Room 3**
- Jump back to Red door (-5, 0).
- Jump to Green door.
- Green door was "front, near" from (0,0) facing East.
- So Green door at (2, 0).
- JumpTo(Green door) -> Agent at (2, 0). Facing East.
- Observe:
- Toilet: Front-slight-right (ESE). Slightly far.
- Fridge: Front-right (SE). Slightly far.
- Basket: Front-slight-left (ENE). Mid distance.
- JumpTo(Basket).
- Basket is ENE from (2,0). Mid (3?).
- Let's say Basket at (5, 1).
- At Basket (5, 1), Facing East:
- Toilet: Front-right (SE). Mid.
- Rotate 90 -> South. At (5, 1), Facing South.
- Observe:
- Airplane: Front-right (SW). Slightly far.
- Toilet: Front-left (SE). Mid.
- Wait. Facing South. Front-Left is SE.
- From Basket (5,1), Toilet is SE.
- Consistent with observation from Door (ESE/SE).
- Fridge: Front (South). Mid.
- Fridge is South of Basket.
- Basket (5, 1) -> Fridge (5, -2)?
- Relation: "airplane is east, near to fridge".
- Relative frame: Facing South = 'North'.
- 'East' relative to 'North' is Right = True West.
- So Airplane is West of Fridge.
- Airplane observed Front-right (SW). Fridge Front (S).
- Airplane is indeed West of Fridge.
- Fridge at (5, -2). Airplane at (3, -2).

**Consolidated Coordinates:**
Room 1:
- Agent Start: (0,0)
- Green Door: (2, 0)
- Red Door: (-5, 0)
- Lego man: (-3, 2) (Front-left from 0,0 N; Front-right from 0,0 W. Wait. W facing N is Left. W facing W is Right. Matches NW).
- Bike: (-3, 1) (South of Lego man).
- Shopping Cart: (2, -3) (SE from 0,0).
- Backpack: (-2, -3) (SW from 0,0).

Room 2:
- Truck: (-7, 2)
- Soda can: (-7, 3) (North of Truck)
- Rubberduck: (-9, 2) (West of Truck)
- Lamp: (-9, 4) (NW of Truck)

Room 3:
- Basket: (5, 1)
- Fridge: (5, -2) (South of Basket)
- Toilet: (7, -1)? (SE of Basket).
- From Door (2,0): Toilet ESE/SE.
- From Basket (5,1) facing E: Toilet SE.
- From Basket (5,1) facing S: Toilet SE.
- Matches.
- Airplane: (3, -2) (West of Fridge).
- From Basket (5,1) facing S: Airplane SW.
- (3, -2) is SW of (5, 1). Matches.

**Refining Coordinates & Distances:**
Green door "near" (0-2) from (0,0). (2,0) fits.
Red door "slightly far" (4-8) from (0,0). (-5,0) fits.

Objects in Room 3:
- Basket mid (2-4) from (2,0). (5,1) is dist sqrt(9+1)=3.16. Fits.
- Fridge mid (2-4) from Basket (5,1). (5,-2) is dist 3. Fits.
- Airplane slightly far (4-8) from Basket (5,1). (3,-2) is dist sqrt(4+9)=3.6. Borderline. Maybe (2,-2)?
- "airplane is east, near to fridge" (Relative East=West). Near=0-2.
- Fridge (5,-2). Airplane (3,-2) is dist 2. Fits.

Room 1 Details:
- Backpack mid (2-4) from (0,0). (-2, -3) -> 3.6. Fits.
- Shopping cart mid (2-4) from (0,0). (2, -3) -> 3.6. Fits.
- "Backpack East (West) of Cart". (-2 vs 2). Fits. Distance 4 (Slightly far? Relation said "near").
- Wait, "backpack is east, near to shoppingcart".
- If they are near, distance <= 2.
- If Agent at (0,0), and both mid (2-4).
- Maybe (0, -3) and (1, -3)?
- Backpack front-right (SW). Cart front-left (SE).
- If Backpack (-1, -3) and Cart (1, -3). Dist 2. Fits "near".
- Angle from (0,0) Facing South:
- (-1, -3): atan(1/3) ~ 18 deg left of South? No, Right of South. South is -y. (-1, -3) is to the right. Correct.
- (1, -3): Left of South. Correct.
- Bins: 18 deg is "front-slight".
- Observation: "Backpack front-right", "Cart front-left".
- "Front-right" is (22.5, 45].
- So angle > 22.5.
- At y=-3, x needs to be > tan(22.5)*3 = 0.41*3 = 1.2.
- So x +/- 1.5?
- Backpack (-1.5, -3). Cart (1.5, -3). Dist 3. Too far for "near".
- Maybe y is smaller? Mid is (2,4).
- y=-2. x +/- 1.
- Angle atan(0.5) = 26 deg. Fits bins.
- Dist sqrt(1+4) = 2.23. Fits mid.
- Dist between them 2. Fits near.
- So Backpack (-1, -2), Cart (1, -2).

Room 1 West Side:
- Red door (-5, 0).
- Lego man "front-left" (NW) from (0,0) N. Angle > 22.5.
- "front-right" (NW) from (0,0) W. Angle < 45 relative to W? No, front-right is (22.5, 45].
- N relative to W is Right (90).
- NW is 45.
- Front-right is 22.5-45. So NW fits.
- Lego man at (-3, 3)?
- From (0,0): (-3, 3) is dist 4.2 (slightly far). Angle 45 (Front-left? No, front-left is 22.5-45. 45 is border. 45.01 is beyond).
- Let's say (-2, 4). Angle atan(2/4)=26 (Front-right N? No N facing. Point is (-2,4). Angle from N is atan(2/4) left = 26 deg left. Bin [-45, -22.5]. Fits Front-Left).
- From West facing (-1, 0, 0): Point (-2, 4). Rel pos (-2, 4).
- Facing West. Forward is -x. Right is +y.
- (-2, 4) is Forward 2, Right 4.
- Angle atan(4/2) = 63 deg.
- Bin Front-Right is (22.5, 45]. 63 is Right or Front-Right?
- 63 is > 45. Should be "Right" (if such bin exists) or "Beyond".
- Wait, "front-right" bin is (22.5, 45].
- My coordinates (-2, 4) don't fit the West view.
- Needs to be closer to x axis.
- Try (-4, 2).
- From (0,0) N: (-4, 2). Dist 4.47 (Slightly far). Angle atan(4/2) = 63 left. Front-Left is [-45, -22.5]. 63 is too wide.
- Try (-2, 3).
- From (0,0) N: Angle atan(2/3) = 33 deg left. Fits Front-Left. Dist 3.6 (Mid). Obs said "Slightly far".
- Maybe (-2, 4). Angle 26. Fits FL. Dist 4.5. Fits SF.
- From (0,0) W: (-2, 4). Forward 2, Right 4. Angle 63. Too wide for FR.
- I need an object that is FL from N and FR from W.
- N view: Angle in [22.5, 45] Left. (True angle 112.5 to 135).
- W view: Angle in [22.5, 45] Right. (True angle 112.5 to 135).
- They are consistent. NW direction.
- True angle 135 is exactly diagonal (-1, 1).
- If strictly inside bins:
- Angle from N (90): 112.5 to 135.
- Angle from W (180): 135 to 157.5? No.
- W facing is 180. Right is +ve. FR is 180 - (22.5 to 45)? No.
- "Positive = clockwise".
- N facing (0 deg? No 0 is front).
- Let's stick to global angles.
- Agent at (0,0).
- N view (Global 0?). Front-Left is [-45, -22.5]. Global 315 to 337.5? Or Counter-Clockwise?
- "Bearing is degree... +: clockwise".
- North is 0? Instructions: "When agent faces north: forward = north". "0° is front".
- So North is 0 global.
- Front-Left: [-45, -22.5]. Global [-45, -22.5] or [315, 337.5]. (NW sector).
- West view (Global -90 or 270).
- Front-Right: [22.5, 45].
- Global = -90 + [22.5, 45] = [-67.5, -45].
- Overlap?
- N view says object in [-45, -22.5].
- W view says object in [-67.5, -45].
- They meet at -45 (True NW).
- So object must be exactly NW? Or slight ambiguity in bins?
- Let's assume (-3, 3).
- Distance "slightly far" (4-8). (-3, 3) is 4.24. Fits.
- "Bike is west, near Lego man".
- Relative West of 'North' (West) is South.
- So Bike is South of Lego man.
- Bike at (-3, 2) or (-4, 3)?
- Bike "front-slight-right" from W. Bin (0, 22.5].
- Global: -90 + (0, 22.5) = [-90, -67.5].
- Lego man at -45.
- Bike is more West than Lego man.
- (-4, 2) angle from origin: atan(2/4) = 26 deg N of W. Global -64. Fits.
- (-3, 3) angle: -45.
- Distance Bike: Mid (2-4). (-4, 2) is 4.47 (Slightly far). (-3, 2) is 3.6 (Mid).
- So Bike (-3, 2). Lego man (-3, 3).
- Relation: "Bike West (South) of Lego man". Fits.
- Distance between them 1. Near. Fits.

Recap:
Agent (0,0) N.
Green Door (2, 0).
Red Door (-5, 0).
Lego man (-3, 3).
Bike (-3, 2).
Backpack (-1, -2).
Shopping cart (1, -2).

Room 2 (from -5, 0):
Truck (-7, 2).
Soda can (-7, 3).
Rubberduck (-9, 2).
Lamp (-9, 4).

Room 3 (from 2, 0):
Basket (5, 1).
Fridge (5, -2).
Airplane (3, -2).
Toilet (7, -1).

Final check on Toilet.
Observed from Green Door (2,0) facing E: Front-slight-right (SE). Slightly far.
Observed from Basket (5,1) facing E: Front-right (SE). Mid.
Observed from Basket (5,1) facing S: Front-left (SE). Mid.
Position (7, -1):
- From (2,0): dx=5, dy=-1. Angle atan(-1/5) = -11 deg. Bin [-22.5, 0] (Front-slight-left?? No, right is +).
- Facing E. Right is South. -y is Right.
- So -11 deg is Right. 11 deg Right.
- Bin [0, 22.5] is Front-slight-right. Fits.
- Dist sqrt(26) = 5.1. Slightly far. Fits.
- From (5,1) facing E: dx=2, dy=-2. Angle -45 deg (Right).
- Bin [22.5, 45] is Front-Right. Fits.
- Dist 2.8. Mid. Fits.
- From (5,1) facing S: dx=2, dy=-2.
- Facing S. Forward -y. Right -x. Left +x.
- (7, -1) is Forward 2 (y 1->-1), Left 2 (x 5->7).
- Angle 45 Left.
- Bin [-45, -22.5] Front-Left. Fits.
- Dist 2.8. Mid. Fits.
Coordinate (7, -1) looks solid.

Facing directions:
Lego man: facing backward (from N). So facing South?
Green door: on front wall (from E). Facing West? (Doors don't usually have facing in JSON, but objects do).
Backpack: facing forward (from S). Facing North?
Shopping cart: facing right (from S). Facing West?
Bike: facing left (from W). Facing South?
Lego man (from W): facing left. Facing South. (Consistent).
Truck: facing backward (from Door W). Facing East?
Rubberduck: facing right (from Door W). Facing North?
Lamp: No facing? (Obs 1: "facing right"? No, from door: "slightly far". From truck: "slightly far". No facing listed? Wait, Observe 1 "facing right" was rubberduck. Truck facing backward. Lamp nothing. Check log).
Log "JumpTo(red door)": "rubberduck... facing right", "truck... facing backward", "lamp... slightly far" (No facing).
Log "JumpTo(truck)": "rubberduck... facing right", "lamp... slightly far".
Log "Rotate(90)": "soda can... near", "lamp... slightly far".
So Lamp has no facing.
Soda can: no facing.
Toilet: facing forward (from Door E). Facing West?
Fridge: No facing? (Log: "fridge: front-right, slightly far". No facing).
Basket: No facing? (Log: "basket: front-slight-left, mid distance". No facing).
Toilet (from Basket): "facing forward". From Basket E -> Facing West? From Basket S -> "facing left" (East?).
- From Basket E (Face E): Toilet (SE) faces "Forward" -> West? (Face towards viewer).
- From Basket S (Face S): Toilet (SE) faces "Left". Relative Left of S is East.
- Contradiction? Forward relative to Agent?
- "facing forward" usually means the object's front is towards the agent. So Object faces West (if agent is East of it? No, agent is West of it).
- Agent at (5,1), Toilet at (7,-1). Agent looks SE. Toilet looks NW?
- "facing forward" = facing the agent.
- "facing left" = facing Agent's left? Or Object's left?
- Usually "facing X" describes the object's intrinsic orientation in global frame, reported relative to agent.
- "facing backward" = facing same direction as agent.
- "facing forward" = facing opposite to agent.
- Agent (E). Toilet faces W.
- Agent (S). Toilet faces N?
- "facing left". Agent (S). Left is E. Object faces E.
- West vs East. Contradiction.
- Maybe "facing left" means Object's Left side is visible?
- Instructions: "Orientation: -forward/backward/right/left (ego) ... When agent faces north: forward = north".
- This section describes how orientation is reported.
- "facing backward" -> Object faces Agent's backward? Or Object faces South?
- Let's assume standard relative-to-agent mapping.
- Case 1: "facing forward" = Object faces Agent.
- Case 2: "facing direction" is absolute but reported relatively.
- Let's check Lego man.
- View N: "facing backward". Agent faces N. Object faces S? Or Object faces N?
- View W: "facing left". Agent faces W. Object faces S?
- If Lego faces S:
- Agent N. S is Backward. Matches.
- Agent W. S is Left. Matches.
- So Lego man faces South.

Check Truck.
- View W (from Door): "facing backward". Agent faces W. Truck faces E.
- Truck faces East.

Check Rubberduck.
- View W (from Door): "facing right". Agent faces W. Right is N. Duck faces N.
- View W (from Truck): "facing right". Agent faces W. Duck faces N.
- Rubberduck faces North.

Check Backpack.
- View S: "facing forward". Agent faces S. Forward is S. But usually forward means "facing the agent" (N)?
- Or "facing forward" means "facing the same way as agent"?
- If Backpack faces S:
- Agent S. Forward is S. Matches.
- If Backpack faces N:
- Agent S. Backward is N.
- Let's compare with Lego man "facing backward" = S (opp to agent N).
- So "Backward" = Opposite. "Forward" = Same?
- Lego man (N view): Agent N. Lego faces S (Backward). Wait. S is opposite to N.
- So "facing backward" means facing opposite to Agent?
- If Agent N, Backward is S. Lego faces S.
- If Agent W, Left is S. Lego faces S.
- This works.
- Backpack (S view): Agent S. "facing forward".
- Forward is S. So Backpack faces South.

Check Shopping cart.
- View S: "facing right". Agent S. Right is W. Cart faces West.

Check Bike.
- View W: "facing left". Agent W. Left is S. Bike faces South.

Check Toilet.
- View E (Door): "facing forward". Agent E. Forward is E. Toilet faces East.
- View E (Basket): "facing forward". Toilet faces East.
- View S (Basket): "facing left". Agent S. Left is E. Toilet faces East.
- Consistent. Toilet faces East.

Check Airplane.
- View S: "facing forward". Agent S. Forward is S. Airplane faces South.

Check objects with no facing:
- Lamp, Soda can, Fridge, Basket.

Final List:
Agent: (5, 1) Facing South.
Green Door: (2, 0).
Red Door: (-5, 0).
Lego man: (-3, 3), Facing South.
Bike: (-3, 2), Facing South.
Backpack: (-1, -2), Facing South.
Shopping cart: (1, -2), Facing West.
Truck: (-7, 2), Facing East.
Rubberduck: (-9, 2), Facing North.
Soda can: (-7, 3).
Lamp: (-9, 4).
Basket: (5, 1).
Fridge: (5, -2).
Toilet: (7, -1), Facing East.
Airplane: (3, -2), Facing South.

JSON Formatting:
Doors don't have facing in schema usually, but "Gate's orientation: report wall position". The schema says "include... gates".
Example doesn't show gates.
"include all observed objects and gates".
I will include them.
Facing for objects is mandatory if observed.

Final JSON Construction.

FINAL ANSWER:
```json
{
"agent": {"position": [5, 1], "facing": "south"},
"green door": {"position": [2, 0]},
"red door": {"position": [-5, 0]},
"lego man": {"position": [-3, 3], "facing": "south"},
"bike": {"position": [-3, 2], "facing": "south"},
"backpack": {"position": [-1, -2], "facing": "south"},
"shoppingcart": {"position": [1, -2], "facing": "west"},
"truck": {"position": [-7, 2], "facing": "east"},
"rubberduck": {"position": [-9, 2], "facing": "north"},
"soda can": {"position": [-7, 3]},
"lamp": {"position": [-9, 4]},
"basket": {"position": [5, 1]},
"fridge": {"position": [5, -2]},
"toilet": {"position": [7, -1], "facing": "east"},
"airplane": {"position": [3, -2], "facing": "south"}
}
```