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: scooter, 2: television, 3: chair, 4: shoes, 5: cap, 6: toilet, 7: backpack, 8: wine, 9: basket, 10: table, 11: plant, 12: bike
Doors: brown door, yellow 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 coordinates (0,0) with an initial orientation facing North. I have a maximum of 20 steps to map the environment, which consists of 3 rooms (Room 1, 2, and 3) and 2 doors (brown, yellow). My goal is to minimize the total cost, where `Observe()` costs 1 and `Query()` costs 2.

In this first step, I have no information about the location of any objects or doors. The rules prohibit using `JumpTo` in the first step. I need to gather visual information to plan my subsequent moves. Since my field of view is 90 degrees, an `Observe()` action will reveal objects in the cone centered on my current facing direction (North). I will perform a simple `Observe()` to scan the area in front of me. This is the most efficient starting move to identify potential navigation targets like objects or doors without incurring unnecessary movement costs or invalid actions.

I am starting the exploration in Room 1 at coordinates (0,0) with an initial orientation facing North. I have a maximum of 20 steps to map the environment, which consists of 3 rooms (Room 1, 2, and 3) and 2 doors (brown, yellow). My goal is to minimize the total cost, where `Observe()` costs 1 and `...

THINK:
I have just started the exploration.
Initial state: Position (0,0), Facing North.
Observation: 'yellow door' is 'front-slight-right' and 'mid distance'.
'mid distance' corresponds to the bin (2, 4]. Let's estimate distance ~ 3.
'front-slight-right' corresponds to the bin (0°, 22.5°]. Let's estimate angle ~ 15°.
Coordinates calculation:
Agent at (0,0) facing North (+y).
Object is at angle +15° (clockwise from North).
x = 3 * sin(15°) ≈ 3 * 0.26 = 0.78 ≈ 1.
y = 3 * cos(15°) ≈ 3 * 0.96 = 2.88 ≈ 3.
So the yellow door is approximately at (1, 3).
The report says "on front wall". Since I'm facing North, the front wall is likely a horizontal wall at some y > 0.
The door connects to another room. I haven't seen any other objects yet.

The JSON map should include the agent and the yellow door.

FINAL ANSWER:
```json
{
"agent": {"position": [0, 0], "facing": "north"},
"yellow door": {"position": [1, 3], "facing": "north"}
}
```

THINK:
I have just started the exploration.
Initial state: Position (0,0), Facing North.
Observation: 'yellow door' is 'front-slight-right' and 'mid distance'.
'mid distance' corresponds to the bin (2, 4]. Let's estimate distance ~ 3.
'front-slight-right' corresponds to the bin (0°, 22.5°]. Let's es...

{
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  }
}

{
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      0
    ],
    "facing": "north"
  }
}

THINK: [The agent is at (0,0) facing North (+y). The 'yellow door' is observed 'front-slight-right' at 'mid distance'.
'Mid distance' corresponds to the interval (2, 4].
'Front-slight-right' corresponds to the bearing interval (0°, 22.5°].
Possible integer coordinates (x, y) relative to agent:
- (1, 3): Distance = $\sqrt{1^2 + 3^2} = \sqrt{10} \approx 3.16$ (fits mid distance). Angle = $\arctan(1/3) \approx 18.4^\circ$ (fits front-slight-right).
- (1, 4): Distance = $\sqrt{17} \approx 4.12$ (slightly far).
- (0, 3): Angle = 0° (front).
- (1, 2): Distance = $\sqrt{5} \approx 2.24$ (mid). Angle = $\arctan(1/2) \approx 26.6^\circ$ (front-right).
The best fit is (1, 3).
Since the door is on the "front wall" (a wall perpendicular to the agent's facing, i.e., running East-West), the door faces North/South. In the local frame, facing the agent is -y.]
FINAL ANSWER: {
"origin": "agent",
"objects": {
"yellow door": {"position": [1, 3], "facing": "-y"}
}
}

THINK: [The agent is at (0,0) facing North (+y). The 'yellow door' is observed 'front-slight-right' at 'mid distance'.
'Mid distance' corresponds to the interval (2, 4].
'Front-slight-right' corresponds to the bearing interval (0°, 22.5°].
Possible integer coordinates (x, y) relative to agent:
- (1,...

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        1,
        3
      ],
      "facing": "-y"
    }
  }
}

{
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        1,
        3
      ],
      "facing": "-y"
    }
  }
}

{
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  }
}

THINK: [The agent is at the position marked `*`. The agent faced North and performed `Observe()`.
Based on the text map and orientation:
- `*` is at a certain coordinate (let's say (x, y)).
- `A` is at (x-1, y+1) and `F` is at (x+1, y+1). Both are within the 45-degree cone relative to North (angles are exactly 45 degrees left and right). They fall into the observable area (FOV is 90 degrees, i.e., +/- 45 degrees). So `A` and `F` are in the observed region.
- `C` is located in the room to the North, behind the North wall/door. The agent is not in the doorway, so vision is blocked by the wall/closed door. Thus `C` is unobserved.
- `E` is to the South-West (row below agent). Outside North-facing FOV. Unobserved.
- `D` is to the South-West (two rows below). Outside FOV. Unobserved.
- `B` is to the South (three rows below). Outside FOV. Unobserved.
Therefore, the points in unexplored/unobserved regions are B, C, D, and E.]
FINAL ANSWER: { "unexplored": ["B", "C", "D", "E"] }

THINK: [The agent is at the position marked `*`. The agent faced North and performed `Observe()`.
Based on the text map and orientation:
- `*` is at a certain coordinate (let's say (x, y)).
- `A` is at (x-1, y+1) and `F` is at (x+1, y+1). Both are within the 45-degree cone relative to North (angles ...

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

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

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

I have observed the yellow door at a "mid distance" to the "front-slight-right". Since my goal is to explore and minimize cost, and I know doors connect rooms, moving to the yellow door is the logical next step. It will allow me to see into the next room (Room 2) while also sitting on the boundary of Room 1. Since I am currently facing North and the door is on the "front wall", retaining my North orientation after jumping will likely direct my view into Room 2. This advances the exploration into a new area.

I have observed the yellow door at a "mid distance" to the "front-slight-right". Since my goal is to explore and minimize cost, and I know doors connect rooms, moving to the yellow door is the logical next step. It will allow me to see into the next room (Room 2) while also sitting on the boundary o...

THINK:
I am currently located at the position of the 'yellow door', which I estimate to be at (1, 3) based on my previous observation from (0,0) (mid distance, front-slight-right). I am facing North.
From this vantage point, I observed four objects in the room ahead (Room 2): a television, a cap, a basket, and a plant.
- The television is observed at 'mid distance' to the 'front-left'. An estimated position of (0, 5) fits this description (distance ~2.2, angle ~-26°). The proximity relation "television is west, near to cap" supports this relative to the cap.
- The cap is observed at 'mid distance' to the 'front-right'. An estimated position of (2, 5) fits this (distance ~2.2, angle ~26°).
- The basket is 'slightly far' to the 'front-slight-right'. An estimated position of (2, 7) fits this (distance ~4.1, angle ~14°). The proximity relation "cap is south, near to basket" holds (Cap at y=5 is south of Basket at y=7).
- The plant is 'slightly far' to the 'front-slight-left'. An estimated position of (0, 7) fits this.
- The television is "facing forward" (relative to my North facing), so it faces North.
- The cap is "facing right" (relative to my North facing), so it faces East.

FINAL ANSWER:
```json
{
"agent": {"position": [1, 3], "facing": "north"},
"yellow door": {"position": [1, 3]},
"television": {"position": [0, 5], "facing": "north"},
"cap": {"position": [2, 5], "facing": "east"},
"basket": {"position": [2, 7]},
"plant": {"position": [0, 7]}
}
```

THINK:
I am currently located at the position of the 'yellow door', which I estimate to be at (1, 3) based on my previous observation from (0,0) (mid distance, front-slight-right). I am facing North.
From this vantage point, I observed four objects in the room ahead (Room 2): a television, a cap, a ...

{
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "yellow door": {
    "position": [
      1,
      3
    ]
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ]
  },
  "plant": {
    "position": [
      0,
      7
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  }
}

THINK: [The agent is at the yellow door facing North (+y in local frame). Observations indicate objects in Room 2.
1. **television**: "front-left" (local -x, +y), "mid distance" (~3m). "facing forward" (local +y). Proximity: West of cap, "near" (<=2m).
2. **cap**: "front-right" (local +x, +y), "mid distance" (~3m). "facing right" (local +x).
3. **basket**: "front-slight-right" (small +x, larger +y), "slightly far" (>4m). Proximity: North of cap (cap is south of basket), "near" (<=2m).
4. **plant**: "front-slight-left" (small -x, larger +y), "slightly far" (>4m).

Estimating coordinates:
- Let Cap be at (1, 3). Distance sqrt(10)≈3.16 (mid). Angle arctan(1/3)≈18° (front-right is >22.5, front-slight-right is <22.5). Wait, front-right is (22.5, 45]. arctan(1/3) is 18, which is slight-right. To be front-right, x needs to be larger relative to y. Maybe Cap at (2, 3)? Angle arctan(2/3)≈33° (front-right). Dist sqrt(13)≈3.6 (mid).
- If Cap is (2, 3), TV is West and Near (<=2). TV at (0, 3) or (1, 3)? If TV is front-left, x must be negative. Let's try Cap (1, 2) [dist 2.2 mid, angle 26 front-right]. TV at (-1, 2) [dist 2.2 mid, angle -26 front-left]. Distance between TV and Cap is 2 (Near). This fits well.
- Basket: Cap (1, 2) is South and Near Basket. Basket at (1, 4)? Dist from origin sqrt(17)≈4.1 (slightly far). Angle arctan(1/4)≈14° (front-slight-right). Fits.
- Plant: front-slight-left, slightly far. Symmetric to basket? (-1, 4). Dist 4.1. Angle -14°. Fits.

Revised Local Coordinates:
- television: [-1, 2], facing +y
- cap: [1, 2], facing +x
- basket: [1, 4]
- plant: [-1, 4]]
FINAL ANSWER: {
"origin": "agent",
"objects": {
"television": {"position": [-1, 2], "facing": "+y"},
"cap": {"position": [1, 2], "facing": "+x"},
"basket": {"position": [1, 4]},
"plant": {"position": [-1, 4]}
}
}

THINK: [The agent is at the yellow door facing North (+y in local frame). Observations indicate objects in Room 2.
1. **television**: "front-left" (local -x, +y), "mid distance" (~3m). "facing forward" (local +y). Proximity: West of cap, "near" (<=2m).
2. **cap**: "front-right" (local +x, +y), "mid ...

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        -1,
        2
      ],
      "facing": "+y"
    },
    "cap": {
      "position": [
        1,
        2
      ],
      "facing": "+x"
    },
    "basket": {
      "position": [
        1,
        4
      ]
    },
    "plant": {
      "position": [
        -1,
        4
      ]
    }
  }
}

{
  "plant": {
    "position": [
      -1,
      6
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      1,
      2
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      1,
      4
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      -1,
      2
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        -1,
        2
      ],
      "facing": "+y"
    },
    "cap": {
      "position": [
        1,
        2
      ],
      "facing": "+x"
    },
    "basket": {
      "position": [
        1,
        4
      ]
    },
    "plant": {
      "position": [
        -1,
        4
      ]
    }
  }
}

{
  "plant": {
    "position": [
      -1,
      6
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      1,
      2
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      1,
      4
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      -1,
      2
    ],
    "facing": "north"
  }
}

THINK: [The agent is at the yellow door (indicated by `*` on the map) facing North, looking into the top room (Room 2). The agent's FOV is 90 degrees (45 degrees to each side).
- **Room 2 (Top):** The agent is at row 8, column 7 (approx).
- Points **C** and **G** are at row 9, columns 4 and 10. The angle to these points is `arctan(3/1) ≈ 71.5°`, which is > 45°. They are outside the FOV.
- Points **I** and **A** are at row 10, columns 4 and 10. The angle is `arctan(3/2) ≈ 56.3°`, which is > 45°. They are outside the FOV.
- Point **D** is at row 11, near column 8 or 9. The angle is small (inside FOV).
- Point **H** is at row 13, column 4? Or 5? `###.H`. It's further away but more central than I/C relative to distance. Wait, H is at x=5 (approx). dy=5. dx=2. Angle `arctan(2/5) ≈ 21.8°`. Inside FOV.
- Thus, **A, C, G, I** are unobserved.
- **Room 1 (Bottom):** The agent started in this room (likely near the bottom center `+` or similar, coordinate (0,0)) and faced North.
- The path from start to the door `*` covers the central column (points B, E, J, K, F).
- Point **L** is in the bottom-left corner (row 2, column 3). The agent never looked West or South-West. From a central starting position facing North, L is outside the 45° cone (`arctan(dx/dy)` where dx is large). Thus, **L** is unobserved.
- **Conclusion:** The unobserved points are the wide corners of the observed room and the blind corner of the starting room.]
FINAL ANSWER:
```json
{
"unexplored": ["A", "C", "G", "I", "L"]
}
```

THINK: [The agent is at the yellow door (indicated by `*` on the map) facing North, looking into the top room (Room 2). The agent's FOV is 90 degrees (45 degrees to each side).
- **Room 2 (Top):** The agent is at row 8, column 7 (approx).
- Points **C** and **G** are at row 9, columns 4 and 10. ...

###############
###.H....######
###......######
###......######
###.....D######
###I....A######
###C....G######
######*########
#....F.########
#....B.#......#
#...JE.#......#
#....K.#......#
#......+......#
#..L...#......#
########......#
###############

You jumped to yellow door. You observe:
• television: front-left, mid distance, facing forward
• cap: front-right, mid distance, facing right
• basket: front-slight-right, slightly far
• plant: front-slight-left, slightly far
Assume your current facing direction is called "north":
• television is west, near to cap
• cap is south, near to basket.
You have a maximum of 18 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to yellow door. You observe:
• television: front-left, mid distance, facing forward
• cap: front-right, mid distance, facing right
• basket: front-slight-right, slightly far
• plant: front-slight-left, slightly far
Assume your current facing direction is called "north":
• television is w...

THINK:
The agent started at (0,0) facing North.
1. Observed `yellow door` at roughly (1,3).
2. Jumped to `yellow door` (1,3), facing North. Observed `television`, `cap`, `basket`, `plant` in Room 2.
- Based on triangulation and relative descriptions:
- `plant` is at (0, 8).
- `basket` is at (2, 7).
- `cap` is at (2, 5).
- `television` is at (0, 5).
3. Jumped to `plant` (0,8), rotated 90° clockwise (facing East). Observed `basket` at (2,7).
- From (0,8) facing East, (2,7) is vector (2, -1) relative to global, which corresponds to forward 2, right 1 in agent frame. Angle ~26.5° (front-right). Distance ~2.2 (mid). This matches the observation.

Current State:
- Agent: Position (0, 8), Facing East.
- Objects:
- `yellow door`: (1, 3)
- `television`: (0, 5)
- `cap`: (2, 5)
- `basket`: (2, 7)
- `plant`: (0, 8)

I need to output the JSON map. I will include the facing direction for the agent. The objects don't have explicit facing directions observed in the last step, but in step 2 `television` was "facing forward" (South, since agent was facing North and saw it front-left? Wait. Agent facing North. Tel front-left (NW). Facing "forward" usually means facing the agent? Or facing same direction? "facing forward" in ego frame?
Actually, the prompt says "facing forward" in the observation list.
Step 2: Agent facing North.
`television`: front-left, facing forward.
`cap`: front-right, facing right.
If "facing forward" means facing the same direction as the agent (North), then TV faces North. If it means facing the agent, it would be South-East?
Usually in these logs:
"facing forward" relative to agent's view usually means the object's front is pointing towards the agent? No, "facing forward" usually means orientation 0 relative to agent. If agent faces North, TV faces North.
"facing right": Agent faces North. Cap faces East.
Let's assume "forward" = North, "right" = East.

Wait, looking at the example: `television: front-left ... facing forward`.
If the agent is at (1,3) facing North. TV is at (0,5).
If TV faces North (same as agent), its back is to the wall? If Room 2 is North of Room 1, usually objects face into the room.
Let's stick to the mapping:
Agent Facing: North.
Object Facing "forward" -> North.
Object Facing "right" -> East.

So:
Television: North.
Cap: East.

The JSON schema asks for `facing` key if the object has a facing direction.
I will include these.

Final Map Content:
Agent: [0, 8], East.
Yellow Door: [1, 3]. (Doors usually don't have "facing" in the output unless specified, but they are on walls. I'll omit facing for door unless I know it's required. The instructions say "include facing key if the object has facing direction". Doors have orientation (e.g. N/S or E/W) but the output format usually just lists position for static objects unless they are agents or directed items. However, the examples show "chair" and "sofa" with facing. I will add facing for TV and Cap. Door orientation is implicit or "north/south" if on horizontal wall. Yellow door is on "front wall" of Room 1 (North wall). So it faces South? Or North? Usually doors connect. I'll leave door facing out to be safe or put standard if needed. The example only shows furniture. I'll stick to furniture.)

Correct positions:
Plant (0,8).
Basket (2,7).
Cap (2,5).
Television (0,5).
Yellow Door (1,3).
Agent (0,8).

FINAL ANSWER:
```json
{
"agent": {"position": [0, 8], "facing": "east"},
"yellow door": {"position": [1, 3]},
"television": {"position": [0, 5], "facing": "north"},
"cap": {"position": [2, 5], "facing": "east"},
"basket": {"position": [2, 7]},
"plant": {"position": [0, 8]}
}
```

THINK:
The agent started at (0,0) facing North.
1. Observed `yellow door` at roughly (1,3).
2. Jumped to `yellow door` (1,3), facing North. Observed `television`, `cap`, `basket`, `plant` in Room 2.
- Based on triangulation and relative descriptions:
- `plant` is at (0, 8).
...

{
  "agent": {
    "position": [
      0,
      8
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ]
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ]
  },
  "plant": {
    "position": [
      0,
      8
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  }
}

THINK:
The agent is currently located at the 'plant' and is facing East (after rotating 90° clockwise from North).
The current observation shows the 'basket' at "front-right" and "mid distance".
In the agent's local reference frame:
- +y is Front (East in global)
- +x is Right (South in global)
- -x is Left (North in global)
- -y is Back (West in global)

"Front-right" corresponds to the angular bin (22.5°, 45°]. This implies the object is in the first quadrant of the local frame, somewhat close to the diagonal.
"Mid distance" corresponds to the Euclidean distance (2, 4].
Possible integer coordinates (x, y) in the local frame that satisfy these constraints:
- (1, 2): Distance $\sqrt{1^2+2^2} \approx 2.24$ (Mid). Angle $\arctan(1/2) \approx 26.6^\circ$ (Front-right).
- (2, 2): Distance $\sqrt{2^2+2^2} \approx 2.83$ (Mid). Angle $45^\circ$ (Front-right boundary).
- (2, 3): Distance $\sqrt{2^2+3^2} \approx 3.61$ (Mid). Angle $\arctan(2/3) \approx 33.7^\circ$ (Front-right).

(1, 2) seems like a plausible and simple estimation. It places the basket forward and to the right.
No facing direction was reported for the basket, so the "facing" key will be omitted.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"basket": {"position": [1, 2]}
}
}
```

THINK:
The agent is currently located at the 'plant' and is facing East (after rotating 90° clockwise from North).
The current observation shows the 'basket' at "front-right" and "mid distance".
In the agent's local reference frame:
- +y is Front (East in global)
- +x is Right (South in global)
- -x...

{
  "origin": "agent",
  "objects": {
    "basket": {
      "position": [
        1,
        2
      ]
    }
  }
}

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

{
  "origin": "agent",
  "objects": {
    "basket": {
      "position": [
        1,
        2
      ]
    }
  }
}

THINK: [The agent started at (1,1) (map coordinates relative to bottom-left floor) facing North.
Step 1: Observed from (1,1) facing North. FOV +/- 45 deg.
- A (1,3): Vector (0,2), Angle 0°. Observed.
- B (5,4): Vector (4,3), Angle 53°. Not Observed.
- C (4,5): Vector (3,4), Angle 37°. Observed.
- L (6,5): Vector (5,4), Angle 51°. Not Observed.
- K (5,1): Vector (4,0), Angle 90°. Not Observed.
- E (6,1): Vector (5,0), Angle 90°. Not Observed.
Step 2: Jumped to Yellow Door (6,7), facing North.
- D (3,8): Vector (-3,1), Angle -71°. Not Observed.
- G (3,9): Vector (-3,2), Angle -56°. Not Observed.
- F (4,11): Vector (-2,4), Angle -26°. Observed.
- I (4,12): Vector (-2,5), Angle -22°. Observed.
- H (4,13): Vector (-2,6), Angle -18°. Observed.
- J (8,8): Vector (2,1), Angle 63°. Not Observed.
Step 3: Jumped to Plant (5,13), Rotate 90 (Facing East).
- J (8,8): Vector (3,-5), Angle -59°. Not Observed.
Unexplored list: B, D, E, G, J, K, L.]
FINAL ANSWER:
```json
{
"unexplored": ["B", "D", "E", "G", "J", "K", "L"]
}
```

THINK: [The agent started at (1,1) (map coordinates relative to bottom-left floor) facing North.
Step 1: Observed from (1,1) facing North. FOV +/- 45 deg.
- A (1,3): Vector (0,2), Angle 0°. Observed.
- B (5,4): Vector (4,3), Angle 53°. Not Observed.
- C (4,5): Vector (3,4), Angle 37°. Observed.
- L...

###############
###.H*...######
###.I....######
###.F....######
###......######
###G.....######
###D....J######
######+########
#......########
#...C.L#......#
#....B.#......#
#A.....#......#
#......+......#
#....KE#......#
########......#
###############

You jumped to plant. You rotated clockwise 90°. You observe:
• basket: front-right, mid distance.
You have a maximum of 17 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to plant. You rotated clockwise 90°. You observe:
• basket: front-right, mid distance.
You have a maximum of 17 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am currently at the `plant` in Room 2 (since the yellow door led to these objects). I just rotated 90 degrees clockwise. My original orientation at the door was North (facing into Room 2). After rotating 90 degrees, I am now facing East.
My observation from the `plant` facing East shows the `basket` to the front-right.
The previous observation from the door showed:
- `television` (front-left relative to door/North -> West)
- `cap` (front-right relative to door/North -> East)
- `basket` (front-slight-right relative to door/North -> North-East)
- `plant` (front-slight-left relative to door/North -> North-West)

I have visited Room 1 (briefly, just the start) and Room 2. I have not seen Room 3 or the brown door yet. The brown door must be somewhere. I need to find the brown door to access Room 3.
From the plant (approx North-West in Room 2), looking East revealed the basket. I haven't scanned the West or South parts of Room 2 fully, or looked back at Room 1 properly, although I came from the yellow door.
The brown door connects to Room 3. It could be in Room 1 or Room 2.
I should look around more in Room 2 to find the other door.
I am at the `plant`. Facing East.
If I rotate to face South or West, I might see more walls of Room 2.
Let's try to jump to another object in Room 2 to get a better vantage point, or rotate.
The `basket` is "front-right" from my current view (facing East) at the `plant`. This puts the basket roughly South-East of the plant, which matches the door view (Plant NW, Basket NE/E... wait. From door: Plant is front-left (NW), Basket is front-slight-right (NE). So Plant is West of Basket. If I am at Plant facing East, Basket should be Front. The observation says "front-right", implying Basket is South-East of Plant).

I need to find the brown door. It wasn't visible from the yellow door looking North into Room 2. It might be on a side wall in Room 2, or back in Room 1.
If I jump to the `basket` and look around, I cover the other side of Room 2.
Or I can jump back to the `yellow door` and look into Room 1 (Rotate 180) to see if the brown door is there.
However, usually, one proceeds 1 -> 2 -> 3. But it could be 1-2 and 1-3.
Let's assume linear 1-2-3 first. If so, brown door is in Room 2.
I haven't seen the brown door in the North view from the yellow door.
Let's check the `basket`. It is "slightly far" from the door, similar to the plant. It's likely deeper in the room.
Moving to `basket` allows me to look at the room from a different angle.
Current pose: At `plant`, facing East.
Action: Jump to `basket`.
Orientation at `basket`: If I don't rotate, I face East.
From `basket`, I should look for the brown door.
Let's try `JumpTo(basket)` and maybe rotate to scan. If the brown door is on the "right" wall of Room 2 (East wall), I might be standing next to it or looking at it.
If I Rotate(90) (face South) or Rotate(-90) (face North).
Let's just Jump to the basket and Observe first, or Rotate.
Actually, if I am at the Plant (NW) and look East, I see the Basket.
I want to maximize coverage.
The `television` and `cap` were "mid distance" from the door, while `plant` and `basket` were "slightly far". This suggests `television` and `cap` are closer to the yellow door (South end of Room 2). `Plant` and `Basket` are further North.
If the brown door is in Room 2, it might be on the North wall (further in) or East/West walls.
I am at the Plant (NW). I looked East.
Let's look North? Or Jump to Basket (NE) and look North/East/West.
Let's Jump to `basket` and `Rotate(-90)` (to face North) to see if there is a door on the far wall. Or `Rotate(90)` (face South) to see back.
Actually, let's just Jump to `basket` and `Observe()` with current East orientation, or maybe rotate to scan better.
If I keep East facing at Basket (which is likely on the East side), I might be staring at the wall.
Let's `JumpTo(basket)` and `Rotate(-90)` to face North. This looks towards the "back" of the room (assuming entry from South).
Wait, if I am at Basket and face North, I look further away from the entry.
Let's try that.

I am currently at the `plant` in Room 2 (since the yellow door led to these objects). I just rotated 90 degrees clockwise. My original orientation at the door was North (facing into Room 2). After rotating 90 degrees, I am now facing East.
My observation from the `plant` facing East shows the `baske...

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

1. **Initial State**:
* Agent at (0, 0), facing North (Room 1).

2. **Observation 1 (from (0,0) facing N)**:
* `yellow door`: "front-slight-right", "mid distance", on "front wall".
* "mid distance" usually implies 3-4 units. "front-slight-right" (0 to 22.5 deg).
* Let's estimate `yellow door` at roughly (1, 3) or (1, 4). Since it's on the "front wall", and usually rooms are aligned, let's assume the wall is at y=something.
* Let's assume the door is at (1, 4) for now to fit "mid distance" (sqrt(1^2+4^2) = ~4.12) or (1,3) (sqrt(10) ~3.16). Let's tentatively place it at (1, 3).

3. **Action 1**: `JumpTo(yellow door)`. Agent is now at the `yellow door`.
* Agent Position: (1, 3).
* Agent Facing: North (unchanged).

4. **Observation 2 (from `yellow door` at (1,3) facing N)**:
* This view looks into Room 2.
* `television`: "front-left" (NW), "mid distance", facing "forward" (South? No, "facing forward" usually means facing the agent, or facing the same way? The instruction says "forward/backward... (ego)". But usually objects have an intrinsic front. "facing forward" relative to agent facing North means the object faces North? Or faces the agent (South)? Standard interpretation: Object's front is aligned with Agent's front. So TV faces North.
* `cap`: "front-right" (NE), "mid distance", facing "right" (East).
* `basket`: "front-slight-right" (NNE), "slightly far".
* `plant`: "front-slight-left" (NNW), "slightly far".
* Proximity info:
* `television` (West of) `cap` (Near).
* `cap` (South of) `basket` (Near).
* Coordinates estimation:
* Agent at (1, 3).
* TV (NW) and Cap (NE) are "mid distance" (approx 3-4 units) and "near" each other (<=2 units).
* If TV is West of Cap, they probably share a Y coordinate or close to it.
* From (1,3) facing N:
* TV: maybe at (-1, 5) or (-1, 6).
* Cap: maybe at (1, 5) or (1, 6) or (2, 5).
* Proximity: TV is West of Cap.
* Cap is South of Basket. Basket is "slightly far" (4-8 units) from door.
* Let's say Cap is at (2, 5). TV at (0, 5). Distance between them is 2 ("near"). Distance from (1,3) is sqrt(1^2+2^2)=2.2 (near/mid boundary) or sqrt(1^2+3^2)=3.16 (mid). Let's approximate TV at (-1, 6) and Cap at (1, 6)? Distance 2. Distance from (1,3) is sqrt(2^2+3^2) ~3.6 (mid).
* Basket is North of Cap ("Cap is South of Basket"). So Basket is at (1, y_basket) where y_basket > 6. Basket is "slightly far" from door (1,3). Say y_basket = 8. Dist = 5 ("slightly far").
* Plant is "front-slight-left" (NNW) and "slightly far". Similar Y to Basket? Maybe (-1, 8) or (-2, 8).

5. **Action 2**: `JumpTo(plant)`, `Rotate(90)`.
* Jump from `yellow door` (1, 3) to `plant`.
* Plant estimated pos: (-2, 8).
* Rotate 90 deg (Clockwise). Initial N -> East.
* Agent Facing: East.

6. **Observation 3 (from `plant` facing E)**:
* `basket`: "front-right", "mid distance".
* If Agent at (-2, 8) facing East:
* Front is East (+x). Right is South (-y).
* "Front-right" is South-East.
* Basket estimated at (1, 8) previously.
* Vector from Plant (-2, 8) to Basket (1, 8) is (+3, 0).
* Relative to East facing: This is "Front".
* Observation says "Front-Right". This implies the Basket is South of the Plant's line of sight.
* So Basket Y < Plant Y.
* Let's adjust.
* From Door (1,3): Cap (1, 6). Basket (1, 8) was the guess. Cap is South of Basket (Correct).
* Plant was "front-slight-left" from Door. Maybe Plant is at (-2, 9)?
* If Plant is (-2, 9) and Basket is (1, 8).
* Vector Plant -> Basket: (3, -1).
* Agent facing East. Front is (1, 0). Right is (0, -1).
* (3, -1) is in the 4th quadrant (Front-Right). Matches "front-right".
* Distance sqrt(9+1) = 3.16 ("mid distance"). Matches.
* So Map Estimate:
* Yellow Door: (1, 3)
* TV: (-1, 6) facing North (forward)
* Cap: (1, 6) facing East (right)
* Basket: (1, 8)
* Plant: (-2, 9)

7. **Action 3**: `JumpTo(basket)`, `Rotate(-90)`.
* Jump to `basket` at (1, 8).
* Rotate -90 (Counter-Clockwise). Previous East -> North.
* Agent Facing: North.

8. **Observation 4 (from `basket` at (1,8) facing N)**:
* `plant`: "front-left", "mid distance".
* Target: Plant (-2, 9).
* Vector Basket -> Plant: (-3, 1).
* Agent facing North. Front is (0, 1). Left is (-1, 0).
* (-3, 1) is mostly Left, slightly Front. "Front-Left" fits (angle is atan(3/1) ~71 deg left, which is > 45 deg?? No.
* Let's check bins.
* Angle 0 is North. (-3, 1) is NNW/WNW.
* Vector (-3, 1). Angle from North = atan2(-3, 1) = -71.5 degrees.
* Bins: [-45, -22.5) FL, [-90, -45) Left? The instructions say: `[-45°,-22.5°)→front-left`. Wait.
* `[-22.5, 0) -> front-slight-left`.
* `(0, 22.5] -> front-slight-right`.
* `(22.5, 45] -> front-right`.
* "otherwise -> beyond-fov".
* Wait. If FOV is 90 degrees (+- 45), then -71.5 degrees is OUT of FOV.
* My coordinates are slightly off if the observation says "front-left".
* "front-left" means angle in [-45, -22.5).
* So the Plant must be more North relative to the Basket.
* Let's adjust Plant/Basket Y.
* If Plant is at (-2, 10) and Basket at (1, 8). Vector (-3, 2). Angle atan(-1.5) ~ -56. Still > 45.
* If Plant is at (-1, 10) and Basket at (1, 8). Vector (-2, 2). Angle -45. Boundary.
* Let's reconsider the previous observation: From Plant (facing East), Basket was "front-right".
* If Plant (-1, 10), Basket (1, 8). Vector (2, -2). Facing East (0 deg relative to grid, but agent orientation).
* Vector (2, -2) relative to East (1, 0) is -45 degrees (Right). "Front-Right" is (22.5, 45]. -45 is 45 degrees Right. Fits "front-right" (22.5 to 45).
* So Plant (-1, 10), Basket (1, 8) fits "Front-Right" from Plant->Basket.
* Does it fit "Front-Left" from Basket->Plant?
* From Basket (1, 8) facing North. Vector to Plant (-1, 10) is (-2, 2).
* Relative to North: Angle -45 (Left). "Front-Left" is [-45, -22.5). Yes, fits.
* Also check Door observation: Door (1, 3). Plant (-1, 10). Vector (-2, 7). Angle atan(-2/7) ~ -16 deg.
* Door observation said Plant was "front-slight-left". [-22.5, 0). -16 fits perfectly.
* Basket (1, 8). Vector (0, 5). Angle 0. Door observation said Basket "front-slight-right". Maybe Basket is at (2, 8)?
* If Basket (2, 8). Vector Door->Basket (1, 5). Angle atan(0.2) ~ 11 deg. Fits "front-slight-right" (0, 22.5].
* Let's check Plant (-1, 10) to Basket (2, 8). Vector (3, -2). Dist ~3.6.
* From Plant facing East. Vector (3, -2). Angle relative to East: atan(-2/3) ~ -33 deg. Fits "front-right" (22.5, 45].
* From Basket (2, 8) facing North. Vector to Plant (-1, 10) is (-3, 2). Angle relative to North: atan(-1.5) ~ -56 deg. This is OUTSIDE "front-left" [-45, -22.5).
* Conflict.
* Basket must be closer to X=-1 or Plant more North.
* Let's pull Basket to (0, 8)?
* Door (1,3) -> Basket (0, 8). Vector (-1, 5). Angle -11 deg. "front-slight-left".
* But Door obs said Basket was "front-slight-right". So Basket X >= Door X (1).
* Let's keep Basket X=1.
* We need Vector Basket->Plant to be within 45 deg of North.
* Basket (1, 8). Plant (x, y). y > 8. |x-1| <= (y-8).
* Let's say Plant (-1, 11). Vector (-2, 3). Angle atan(-0.66) ~ -33 deg. Fits "front-left" [-45, -22.5).
* Check Plant (-1, 11) facing East -> Basket (1, 8). Vector (2, -3).
* Relative to East: atan(-3/2) ~ -56 deg (Right-Back). This is "front-right" (22.5, 45]? No, >45.
* I need a configuration that satisfies both.
* Plant (P), Basket (B).
* P -> B (facing E): Angle(P->B) - 90 in [22.5, 45]. -> Angle(P->B) in [112.5, 135] (South-East).
* B -> P (facing N): Angle(B->P) - 0 in [-45, -22.5]. -> Angle(B->P) in [-45, -22.5] (North-North-West).
* Angle(B->P) = alpha. Angle(P->B) = alpha + 180.
* If alpha in [-45, -22.5] (e.g., -30 aka 330), then P->B is 330-180 = 150.
* 150 relative to East (90) is +60 (Right). 60 is > 45. "beyond-fov"? Or "front-right" is up to 45.
* Maybe the bins are labeled differently in my head?
* "front-right": (22.5, 45].
* This implies I can't see it if it's > 45.
* Wait, the instruction says: `[-45°,-22.5°)→front-left ... (22.5°,45°]→front-right, otherwise→beyond-fov`.
* So objects MUST be within 45 degrees of center.
* So P->B relative to East must be <= 45. (Angle -45 to +45 relative to East). i.e. Global angle 45 to 135.
* B->P relative to North must be <= 45. (Angle -45 to +45 relative to North). i.e. Global angle -45 to +45.
* So B is SE of P. P is NW of B.
* If P->B is SE (e.g. -45 rel East, so global -45 or 315? No. East is 90. Right turn is negative. Front-Right is 0 to 45 deg clockwise. 90-0 to 90-45 -> 90 to 45 global?
* Coordinate system: North is +y. East is +x.
* Angle 0 is Front.
* Facing East (Global +x). Front is +x. Right is -y.
* "Front-Right" (22.5 to 45 deg clockwise). Global direction: 0 deg (East) - 22.5 = -22.5. To -45.
* So Vector P->B has angle in [-45, -22.5] global. (SE).
* Facing North (Global +y). Front is +y. Left is -x.
* "Front-Left" (-45 to -22.5 deg counter-clockwise? No. Signs: + is clockwise, - is counter.
* Inst: `[-45°,-22.5°)→front-left`. Negative is Counter-Clockwise.
* Facing North (90 deg? No, usually North is 0 or 90 depending on convention. Here "0 is front". Let's use relative).
* Relative to North: [-45, -22.5].
* So Vector B->P has angle relative to North in [-45, -22.5]. (Global: N + CCW = NW).
* So P is NW of B. B is SE of P.
* This is consistent.
* Let's re-verify coordinates.
* B->P: NW. Angle ~ -30 deg (from N). Vector (-1, 2) -> atan(-0.5) = -26. Fits.
* P->B: SE. Vector (1, -2). Facing East.
* East is (1, 0). Vector (1, -2). Angle from East?
* Dot product? Angle = atan(-2/1) = -63.
* Relative to East, -63 is > 45. Too far right.
* Need B->P to be steeper? (-1, 3)? Angle atan(-0.33) = -18. (Front-slight-left).
* Need P->B to be shallower? Vector (2, -1)? Angle atan(-0.5) = -26.
* Facing East. -26 is "Front-Right" (22.5 to 45? No. 26 is in 22.5-45).
* So P->B vector (2, -1) works.
* Then B->P is (-2, 1).
* Facing North. (-2, 1). Angle atan(-2) = -63. Too far Left.
* This is a geometric squeeze.
* P->B: (dx, dy). dy < 0. dx > 0.
* Facing East: atan(dy/dx). Needs to be in [-45, -22.5] (Right is +? "0 is front. +: clockwise". So Front-Right is POSITIVE angle. Front-Left is NEGATIVE).
* Okay. Facing East. Right is South. Clockwise from East is South.
* So P->B should have angle +22.5 to +45 relative to East.
* Global angle: East is 0 (math) or 90 (nav)? Let's stick to relative.
* Vector (dx, dy).
* Facing East (1, 0). Rotate vector by -90? No.
* Angle of vector (dx, dy). East is 0.
* We want angle in [-45, -22.5] (Clockwise is positive? "0 is front. +: clockwise". So Front-Right is POSITIVE [22.5, 45]. Front-Left is NEGATIVE).
* P->B (facing East). We want Front-Right. So angle +22.5 to +45.
* East is 0. So vector angle is -22.5 to -45 (Math convention: CCW is +).
* Wait, let's use the provided sign convention.
* Front=0. + is Clockwise. - is CCW.
* Facing East. Front is East.
* Front-Right is Clockwise. So South-ish.
* So P->B is South-East.
* Angle(P->B) relative to East is in [22.5, 45].
* So |dy|/dx should be tan(22.5) to tan(45). 0.41 to 1.
* So 0.41 < |dy|/dx < 1.
*
* B->P (facing North).
* Front is North.
* Front-Left is [-45, -22.5] (CCW).
* So P is North-West of B.
* Angle relative to North is [-45, -22.5].
* So |dx|/dy should be tan(22.5) to tan(45). 0.41 to 1.
*
* Let vector B->P be (-dx, dy).
* Ratio dx/dy in [0.41, 1].
* Vector P->B is (dx, -dy).
* Ratio dy/dx in [0.41, 1].
* So we need x/y in [0.41, 1] AND y/x in [0.41, 1].
* This is possible if x roughly equals y.
* Example: dx=3, dy=4. dx/dy = 0.75. dy/dx = 1.33 (Fail).
* Example: dx=3, dy=3. dx/dy=1. dy/dx=1.
* If dx=dy, Angle is 45.
* 45 is boundary of "front-right" (22.5, 45].
* -45 is boundary of "front-left" [-45, -22.5).
* So if |dx| ~ |dy|, it works.
* So Plant and Basket are roughly diagonal.
* Let's place them:
* Basket at (2, 8). Plant at (0, 10). (dx=2, dy=2). Distance 2.8.
* Door (1, 3).
* Basket (2, 8): Vector (1, 5). Angle ~11 deg (Right). Fits "front-slight-right".
* Plant (0, 10): Vector (-1, 7). Angle ~ -8 deg (Left). Fits "front-slight-left".
* Coordinates seem solid:
* Yellow Door (1, 3).
* Basket (2, 8).
* Plant (0, 10).
* TV (-1, 6)?
* Cap (1, 6)?
* TV west of Cap. TV (-1, 6) -> Cap (1, 6). Dist 2. Near.
* Door (1, 3) -> TV (-1, 6). Vector (-2, 3). Angle atan(-0.66) = -33. Front-Left. Correct.
* Door (1, 3) -> Cap (1, 6). Vector (0, 3). Angle 0. Front.
* Observation said Cap "front-right".
* Maybe Cap is (2, 6)? Vector (1, 3). Angle 18. Front-slight-right.
* Obs said "front-right" (22.5+).
* Need angle > 22.5. atan(1/3) = 18. Not enough.
* Need Cap more right or closer. Cap (2, 5)? Vector (1, 2). Angle 26. Fits.
* If Cap (2, 5) and TV (0, 5).
* Door -> TV (0, 5). Vector (-1, 2). Angle -26. Front-Left. Fits.
* Cap (2, 5) South of Basket (2, 8). Fits.
* TV (0, 5) West of Cap (2, 5). Fits.
*
* Current Map:
* Yellow Door: (1, 3).
* TV: (0, 5). Facing North.
* Cap: (2, 5). Facing East.
* Basket: (2, 8).
* Plant: (0, 10).
* Agent is at Basket (2, 8) facing North.

* Goal: Find brown door.
* I've seen Room 2 objects (TV, Cap, Basket, Plant).
* I haven't seen the Brown Door.
* It might be on the North Wall of Room 2? Or East/West.
* From Basket (2, 8) facing North, I observed Plant (0, 10).
* I did NOT observe a door.
* Maybe the door is in Room 1?
* Or maybe I need to Query? Or look in a different direction?
* If Brown Door is in Room 2, and I haven't seen it:
* From Door (looking N): saw TV, Cap, Basket, Plant. No Brown Door.
* From Plant (looking E): saw Basket. No Brown Door.
* From Basket (looking N): saw Plant. No Brown Door.
* The only places left are:
* - South wall of Room 2 (Back towards Room 1, maybe brown door is there too? Unlikely).
* - West wall of Room 2 (Blocked by Plant/TV?).
* - East wall of Room 2 (Blocked by Cap/Basket?).
* - North wall of Room 2 (Beyond Plant/Basket).
* - Room 1 (I only did one observe there).
* In Room 1, I saw Yellow Door. I didn't see Brown Door.
* Maybe Brown Door was outside FOV in Room 1?
* Room 1 Obs: "yellow door: front-slight-right".
* FOV is 90 (-45 to +45).
* If Brown Door was to the Left or far Right in Room 1, I missed it.
* Strategy: Explore Room 2 fully. If not found, go back to Room 1.
* Currently at Basket (2, 8) facing North.
* The Plant is at (0, 10).
* Usually 3 rooms. Room 3 connects to Room 2 or Room 1.
* If Brown Door is in Room 2, it's likely on a wall.
* Let's check the West or East wall or North wall closely.
* I am at (2, 8). Facing North.
* I can Rotate to face South to see the entry area again, or West.
* Or Jump to Plant (0, 10) and look North/West.
* If I Jump to Plant (0, 10) and face West or North.
* Let's try to look for the door.
* I will Jump to `plant` again? No, I was there. I looked East.
* I should look West or North from Plant.
* The cost is important.
* Let's think about Room 1.
* Maybe I should Query `yellow door` to fix coordinates?
* Or just Explore.
* I'll Jump to `plant` and `Rotate(-90)` (to face North) or `Rotate(180)` (to face West? No, I'm facing N at Basket. To face West at Plant: Jump(Plant), Rotate(-90) -> West).
* Wait.
* Current: At Basket, Facing North.
* Action: `JumpTo(plant)`.
* Arrive at Plant (0, 10). Facing North.
* If I `Observe`, I look North.
* This covers the North wall of Room 2.
* This seems good.

FINAL ANSWER:
{
"agent": {"position": [2, 8], "facing": "north"},
"yellow door": {"position": [1, 3]},
"television": {"position": [0, 5], "facing": "north"},
"cap": {"position": [2, 5], "facing": "east"},
"basket": {"position": [2, 8]},
"plant": {"position": [0, 10]}
}

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

1. **Initial State**:
* Agent at (0, 0), facing North (Room 1).

2. **Observation 1 (from (0,0) facing N)**:
* `yellow door`: "front-slight-right", "mid distance", on "front wall".
* "mid distance" usually impl...

{
  "agent": {
    "position": [
      2,
      8
    ],
    "facing": "north"
  },
  "yellow door": {
    "position": [
      1,
      3
    ]
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      8
    ]
  },
  "plant": {
    "position": [
      0,
      10
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      7
    ],
    "facing": "north"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      7
    ],
    "facing": "north"
  }
}

THINK:
I am currently located at the `basket`.
My previous action was `JumpTo(basket)` followed by `Rotate(-90)`.
At the `plant`, I was facing East. `Rotate(-90)` (counter-clockwise) means I am now facing **North**.
My observation is:
- `plant`: front-left, mid distance.

I need to construct the **Local Cognitive Map** relative to me (the agent) as the origin (0,0) facing +y.
- Agent is at (0,0) facing +y (North).
- `plant` is "front-left".
- "Front" means +y.
- "Left" means -x.
- "Mid distance" usually implies a Euclidean distance in (2, 4].
- Based on the previous observation from the yellow door:
- Plant was front-slight-left.
- Basket was front-slight-right.
- They seemed roughly symmetric or at least separated by some width.
- From Plant facing East, Basket was front-right.
- Now from Basket facing North, Plant is front-left.
- Let's estimate coordinates. If Plant is front-left, maybe x=-2, y=2? Or x=-3, y=1?
- "Mid distance" is >2.0. If x=-2, y=2, distance is sqrt(8) ~ 2.8, which fits.
- Let's assign `plant` to `[-2, 2]`.
- The observation didn't specify the facing of the plant itself, so I won't include "facing" for the plant.

Wait, I need to be precise about "front-left".
Bins: [-45, -22.5). This is 45 degrees left of center roughly.
If I put it at (-2, 2), angle is +45 deg (Left is +90? No, usually angles are counter-clockwise. Front is 0. Left is +90. Front-left is [22.5, 67.5]? No, the prompt says "front-left" is [-45, -22.5).
Wait, prompt says: "Egocentric angle bins (0° is front): [-45°,-22.5°)→front-left".
This implies negative angles are to the LEFT?
Standard math: 0 is East. But here 0 is Front.
Usually, Left is Positive. But prompt says "[-45°,-22.5°)→front-left". This implies Left is NEGATIVE degrees?
Let's check the prompt again: "Bearing is a degree in [-180, 180]; 0° is front. +: clockwise, -: counterclockwise."
Usually + is CCW. Here + is Clockwise.
So:
0 = Front
+90 = Right
-90 = Left
So "front-left" is indeed [-45, -22.5). Wait.
If 0 is front and - is CCW (Left), then -45 is Front-Left. Correct.
So angle is roughly -30 degrees.
If I use (-1, 2), angle is atan2(x, y).
x is right (+), y is front (+).
atan2(-1, 2) is approx -26 degrees. This fits [-45, -22.5).
Distance sqrt(1+4) = 2.23 (mid distance > 2). Fits.
So I will place `plant` at `[-1, 2]`.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"plant": {"position": [-1, 2]}
}
}
```

THINK:
I am currently located at the `basket`.
My previous action was `JumpTo(basket)` followed by `Rotate(-90)`.
At the `plant`, I was facing East. `Rotate(-90)` (counter-clockwise) means I am now facing **North**.
My observation is:
- `plant`: front-left, mid distance.

I need to construct the **L...

{
  "origin": "agent",
  "objects": {
    "plant": {
      "position": [
        -1,
        2
      ]
    }
  }
}

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

{
  "origin": "agent",
  "objects": {
    "plant": {
      "position": [
        -1,
        2
      ]
    }
  }
}

THINK:
I need to identify which candidate points (A-Z) are in unexplored regions based on the map provided and my exploration history.

**Current State & History:**
1. **Start:** Room 1, (0,0), facing North. Observed `yellow door`.
2. **Move 1:** Jumped to `yellow door`. Observed `television`, `cap`, `basket`, `plant` in Room 2. The `yellow door` is on the "front wall" of Room 1, so it's the connection between Room 1 (South) and Room 2 (North).
- Observation from door (facing North):
- `television` (West/Left)
- `cap` (East/Right)
- `plant` (North-West/Front-Left)
- `basket` (North-East/Front-Right)
3. **Move 2:** Jumped to `plant` (North-West). Rotated 90 deg (facing East). Observed `basket`.
4. **Move 3:** Jumped to `basket` (North-East). Rotated -90 deg (facing North).
- My current position is at `basket`. The map shows `*` at the `basket`'s location.
- I am facing North. My FOV is 90 degrees (North-West to North-East).

**Map Analysis:**
The map shows the layout. The agent `*` is at `B`'s location (roughly). Wait, looking at the map:
The map has walls `#`, floors `.`, doors `+`, and the agent `*`.
The agent is near `B`. Actually, `B` is labeled right next to `*`.
There is a door `+` below the agent's room (Room 2). This is the `yellow door` connecting to the room below (Room 1).
There is another door `+` in the room below (Room 1), on the right wall? No, looking at the bottom room:
Room 1 is the bottom-left area defined by `#` boundaries.
There is a door `+` at the top of Room 1 leading to Room 2. This matches the `yellow door`.
There is another door `+` on the *right* wall of Room 1? Let's check the map structure.
Bottom section:
```
#...G.C########
#......#......#
#....F.#......#
#J.....#......#
#.....H+......#
#.L....#......#
########......#
```
Wait, the `+` is at `H`. This looks like a door connecting the left room (Room 1) to a room on the right (Room 3?). Or is `H` just a candidate next to a door? The `+` is part of the wall `########......#`. No, the `+` is vertical in the wall `......H+......`. It looks like a door on the East wall of Room 1.
There is another `+` between the top room (Room 2) and bottom room (Room 1).

**Unexplored Analysis:**
My vision history:
1. **Room 1 (Bottom Left):**
- Initial `Observe()` facing North from start. Saw `yellow door` (the top door).
- My FOV was a cone North.
- Area covered: The central/northern part of Room 1 up to the door.
- Candidates in Room 1: `G`, `C`, `F`, `J`, `H`, `L`.
- `G` is central/north. Likely seen.
- `C` is central/north. Likely seen.
- `F` is central. Likely seen.
- `J` is far West/Left. Might be outside the North-facing cone from (0,0) if wide enough, but `J` is on the wall. The cone is 90 degrees. If I am at (0,0) facing North (Y+), I see Y > |X|. `J` looks like it has a high negative X relative to center? No, coordinates start bottom-left.
- Let's assume the "start" (0,0) was somewhat central or bottom. The prompt said "initial position is in room 1 and you face north... origin (0,0)".
- The map shows candidates.
- `H` and the door near it: The door is on the East wall. From (0,0) facing North, the East wall is on the right. 45 degrees. I might have seen it? But I only reported `yellow door`. I did not report `brown door`. If the East door is the `brown door`, I haven't seen it yet. Therefore, the area around the East door (`H`) and the room beyond it are unobserved.
- `L` is in the bottom-left corner. From (0,0) facing North, this is behind me or to the extreme left. Likely unobserved.
2. **Room 2 (Top):**
- Jumped to `yellow door` (facing North). Saw `TV` (West), `Cap` (East), `Plant` (NW), `Basket` (NE).
- Jumped to `Plant` (facing East). Saw `Basket`.
- Jumped to `Basket` (facing North). Just observed.
- Candidates in Room 2: `A`, `B`, `I`, `K`, `D`, `E`.
- `B` is near the basket (current pos). Observed.
- `A` is North of Basket. Current observation (facing North from Basket) should see `A`.
- `I` is South of Basket? No, looking at map: `B*` is near top right. `A` is top left?
Let's trace the map grid.
`###..A...######` (Row ~13)
`###...B*.######` (Row ~12) - `B` and Agent are here.
`###....I.######` (Row ~11)
`I` is below `B`.
- From `yellow door` (bottom of Room 2), I looked North. I saw `Plant` (West side) and `Basket` (East side). `I` is in the middle/East. Likely seen.
- `D` and `E` are near the door `+`. `D` (West), `E` (East). Seen from door.
- `K` is on the West wall. `Plant` was front-left (West). `K` might be near `Plant` or behind it.
- Candidate `A` is North-West of `B`? Row 13 vs 12. `A` is higher. If I am at `B` facing North, I see `A`.
- So Room 2 is mostly explored.
3. **Room 3 (Bottom Right?):**
- The map shows a space to the right of Room 1.
- Candidates: No labels visible in the text block for the right side, but the map shows `......` to the right of `H+`.
- Wait, are there candidates in the unconnected black void or the other room?
- The map ascii shows:
```
#.....H+......#
#.L....#......#
########......#
```
This implies a room to the right of Room 1.
- I have never been there. I haven't seen the door connecting to it (presumably near `H`).
- Therefore, any points in Room 3 are unexplored. But there are no letter labels in Room 3 in the provided ascii snippet?
Wait, let me look closer at the ASCII.
`#...G.C########` -> Room 1 top part.
`#......#......#` -> Room 1 and Room 3 separated by wall?
`#....F.#......#`
`#J.....#......#`
`#.....H+......#` -> Door `+` connects Room 1 and Room 3.
`#.L....#......#`
There are no letters A-Z inside the right room (Room 3).
So I only need to evaluate A-L.

**Evaluating A-L:**
- **Room 2 (Top):**
- `A`: North of `Basket`. I am at `Basket` facing North. I see it now. (Observed).
- `B`: At `Basket`. (Observed).
- `I`: South of `Basket`. Seen from `yellow door` looking North. (Observed).
- `K`: West wall. Seen from `yellow door` (saw Plant/TV on that side). (Observed).
- `D`, `E`: Near entry. Seen. (Observed).
- *Conclusion for Room 2:* All likely observed.

- **Room 1 (Bottom):**
- I started here facing North.
- Cone: (0,0) facing +Y.
- `G` (Top Center): Seen.
- `C` (Top Right): Seen.
- `F` (Center): Seen.
- `J` (West Wall): From origin facing North, West wall is 90 deg left. Peripheral. Might be seen or not. The cone is usually +/- 45 deg. If `J` is strictly > 45 deg, it's blind. However, `Observe` usually catches things in the room if not blocked. But strictly, FOV is 90 deg. (0,0) to `J`? If `J` is (-x, y), angle is atan(y/-x). If angle > 45, unseen.
- `L` (South West): Behind/Left of start. Unseen.
- `H` (South East, near door): Unseen. The door near `H` was not reported in the first `Observe`. The first `Observe` only reported `yellow door` (North). So the East door and `H` were definitely missed.

**Candidates to select:**
- `L`: Behind/Left of start.
- `H`: Right/South of start (East wall). Missed in first view.
- `J`: West wall. Likely missed if FOV is strict 90 deg front.
- `F`: Center. Seen.
- `C`, `G`: Near yellow door. Seen.

Let's refine `J`.
If I am at (0,0) facing North. `yellow door` is "front-slight-right".
`J` is on the left wall. `L` is below `J`.
If `yellow door` is front-slight-right, I might be slightly left of center?
If I missed the East door (near `H`), I definitely missed `L`.
`J` is likely on the edge of FOV or out.
However, `H` is the most critical as it marks the unexplored door. `L` is in the back corner.
Are `A`, `C` considered unexplored?
`A` is in front of me now. `Observe` reports usually cover the current view. The prompt asks for "unexplored/unobserved regions". The current `Observe` at `Basket` facing North *just happened*. It reported `plant` (front-left). It did not report `A` (if `A` is an object). But `A` is a location. If there's nothing there, it's empty space. I have "observed" the space.
However, the Fog Probe usually asks what is *currently* unknown or in the fog *before* the current step's integration? No, it asks based on the provided map which implies current knowledge.
Wait, "Select the points that are located in unexplored/unobserved regions."
I am *at* `B`. I face North.
I see `A`'s region.
I have seen `D`, `E`, `I`, `K` from the door.
In Room 1, I saw the cone towards `yellow door` (`G`, `C` area).
I did NOT see the corners `J`, `L`, `H`.
So `H`, `J`, `L` are candidates.
Also `C`? `C` is near the yellow door. I jumped to the yellow door. I must have seen the area around it. `C` is likely observed.

Let's check `A`. I am at `B` facing North. `A` is directly North. I definitely see it.
Let's check `I`. Between `B` and door. Passed through it. Seen.
Let's check `K`. West side. Saw Plant there. Seen.

Focus on Room 1.
`H`: Near the hidden brown door. Unobserved.
`L`: Bottom left corner. Unobserved.
`J`: West wall. Likely Unobserved.
`F`: Center. Likely Observed.
`G`, `C`: Top. Observed.

Wait, is `brown door` observed? No. It's likely near `H`.
So `H` is definitely in the fog.
`L` is in the fog.
`J` is in the fog.

What about `F`? If I stood at (0,0) and looked North, `F` is in the middle. I saw through it.

So `H`, `J`, `L`.

Let's verify the map labels again.
Room 1:
`G`, `C`: Top.
`F`: Middle.
`J`: Left.
`H`: Right (near door).
`L`: Bottom Left.

Room 2:
`A`: Top.
`B`: Top Right (Agent).
`I`: Middle Right.
`K`: Left.
`D`, `E`: Bottom.

Status:
Room 2 is fully explored (entered, looked around).
Room 1 is partially explored (looked North from start, then left).
Back corners of Room 1 (`L`, `H`, `J`) are the main unexplored areas.

Final selection: `H`, `J`, `L`.
Maybe `C`? No, `C` is near the door I used.

Wait, "You observe: plant...". Nothing else reported in Room 2 North view?
From `Basket` looking North, I saw `plant` (front-left).
The map shows `A` is straight ahead? Or empty space?
If `A` is just a point in space, I see it.
So Room 2 is clear.

Room 1:
I never looked South or East/West in Room 1.
I only looked North.
Cone covers `F`, `G`, `C`.
Blind spots: `J` (West), `L` (South West), `H` (South East), and the corner behind me.
So `H`, `J`, `L` are valid.
Is `F` observed? It's on the path to the door. Yes.

Let's reconsider `J`. If I am at (0,0) and `J` is (0, something) or (-2, 2)?
If I am at (0,0), `J` is to the left. 90 degrees.
FOV is 90 degrees total (-45 to +45).
So `J` (at -90 or similar) is definitely NOT seen.
`H` (at +something) is likely not seen.
`L` (behind) is not seen.

So `H`, `J`, `L` are the unexplored points.

The map provided in the prompt shows:
`#...G.C########`
`#......#......#`
`#....F.#......#`
`#J.....#......#`
`#.....H+......#`
`#.L....#......#`
`########......#`

The door is near `H`. Since I haven't found the brown door yet, and it's likely that `+` near `H`, `H` is definitely unexplored.
`L` is deep in the corner. Unexplored.
`J` is on the wall. Unexplored.

What about `C`? It's right next to the wall `C########`.
I saw `yellow door` at "front-slight-right".
The yellow door is likely the gap above `G`/`C`.
If I saw the door, I saw `C`.

Result: `H`, `J`, `L`.
Are there any in Room 2?
`K` is far left. Saw `plant` there.
`A` is far top. Current view covers it.

I will output `H`, `J`, `L`.

Double check logic.
Start -> Look North. Saw `yellow door` (Front-Right).
FOV: [-45, 45].
Objects at > 45 deg or < -45 deg are unseen.
`J` is West (Left). Angle ~ -90. Unseen.
`L` is South-West. Angle ~ -135. Unseen.
`H` is East/South-East. Angle ~ 90 or 135. Unseen.
`F` is North. Seen.
`G` is North. Seen.
`C` is North-East. Inside 45? `yellow door` was front-slight-right (0 to 22.5). `C` is likely near it. Seen.

Room 2:
I am at `Basket` (B).
Saw `Plant` (K area).
Saw `TV`, `Cap` (D/E area).
Saw `Basket` (I area).
Facing North now. Seeing `A`.

So `H`, `J`, `L` are the best candidates.

Refining `J`:
If `J` is at `x < 0` relative to start, and I faced `y+`.
Yes, `J` is unseen.

Refining `H`:
`H` is near the door to Room 3.
I haven't seen Room 3.
`H` is unseen.

Refining `L`:
`L` is behind. Unseen.

Are there any others?
`A`, `B`, `C`, `D`, `E`, `F`, `G`, `I`, `K` are likely seen.

Final check on `C`.
`C` is to the right of `G`. The wall starts there.
If door is at `G`...
Prompt: "yellow door: front-slight-right".
This implies door is at angle > 0.
If `C` is further right, it might be > 22.5.
But I jumped to the door.
When at the door, I look into Room 2. I don't look back at `C` in Room 1.
However, the first `Observe` covered the door. `C` is adjacent.
Usually, "unexplored" means "not yet visited or seen".
If `C` was in the FOV, it's observed.
Given `yellow door` (mid dist), `C` is likely same distance.
I'll assume `C` is observed.

So `H`, `J`, `L`.

Wait, looking at the map again.
`#...G.C########`
The top row of Room 1.
If `yellow door` is the gap, it's near `G`.
`C` is in the corner to the right of the door.
If door is front-slight-right (0-22.5), and `C` is further right...
Maybe `C` is observed.

I'll stick with `H`, `J`, `L`.

Wait, look at `F`.
`F` is in the middle of Room 1.
Start (0,0) -> Door (Mid Dist).
`F` is "Near" or "Mid"?
If I look North, I see `F`.
It's observed.

What about `A`?
I am at `B` (Row 12). `A` is Row 13.
I am facing North.
I definitely see `A`.

So `H`, `J`, `L`.

Is there a `M`? No.
Is `G` observed? Yes, near door.

One edge case: `K`.
In Room 2, `Plant` is at `K`?
Saw `Plant` from door (front-left).
Saw `Plant` from `Basket`? No, saw `Plant` from `Basket` as "front-left".
So `K` is observed.

Final list: H, J, L.

Wait, looking at the string "###..A...######". `A` is surrounded by dots.
"###...B*.######". `B` is where I am.
"###....I.######".
The map shows `A` is in the top-left-ish of the room?
`B` is to the right.
If I am at `B` facing North, `A` is to my Left (West).
Coordinate-wise:
Row 13: `..A...`
Row 12: `...B*.`
`A` is column ~5. `B` is column ~7.
`A` is North-West of `B`.
My facing is North.
FOV: North-West to North-East.
`A` is in FOV.
So `A` is observed.

Okay, H, J, L.

One more check on `J`.
`J` is Row 9?
`#J.....#......#`
If I started at (0,0) (Row 6?), and looked North.
`J` is Left. Unobserved.

Okay.

FINAL ANSWER:
{
"unexplored": ["H", "J", "L"]
}

THINK:
I need to identify which candidate points (A-Z) are in unexplored regions based on the map provided and my exploration history.

**Current State & History:**
1. **Start:** Room 1, (0,0), facing North. Observed `yellow door`.
2. **Move 1:** Jumped to `yellow door`. Observed `television`, `ca...

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

You jumped to basket. You rotated counterclockwise 90°. You observe:
• plant: front-left, mid distance.
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to basket. You rotated counterclockwise 90°. You observe:
• plant: front-left, mid distance.
You have a maximum of 16 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am currently at the `basket` in Room 2. I just rotated to face North.
Observation: `plant` is front-left.
This confirms `plant` is to the West of `basket` (since I face North).
I still haven't seen the `brown door`.
I have observed `television`, `cap`, `plant`, `basket` in Room 2.
I observed `yellow door` in Room 1.
I haven't fully explored Room 1 (only saw yellow door).
I haven't found the connection to Room 3.
The brown door must be somewhere.
Possibilities:
1. Brown door is in Room 2, but I missed it. (Maybe on the East wall, West wall, or North wall but outside FOV).
- From yellow door (facing North), I saw TV, Cap, Basket, Plant. No brown door.
- At Plant (facing East), I saw Basket.
- At Basket (facing North), I see Plant.
I haven't looked South from deep in the room (Basket/Plant).
I haven't looked East from Basket (I was facing East before rotation, but I didn't Observe from Basket facing East. I Observed from Plant facing East).
I haven't looked West from Plant (I was facing North-ish at Plant? No, I jumped to Plant and rotated 90 to face East. I didn't observe facing West or North from Plant).

Wait, at the yellow door, I faced North. I saw Plant (Front-slight-left) and Basket (Front-slight-right). This implies they are generally North of the door.
If the brown door was on the North wall, I might have seen it from the yellow door if it was central. If it's on the side, maybe not.
If the brown door is in Room 1, I need to go back.

Let's consider the layout. Room 1 -> Yellow Door -> Room 2.
Is there a Room 3 connected to Room 2? Or Room 1?
Usually "Room 1, room 2, room 3 connected by doors". Could be linear 1-2-3 or star 2-1-3 or 1-2 & 1-3.

If I missed the brown door in Room 1: I started at (0,0) facing North. Saw yellow door (front-right). I didn't look Left (West) or Back (South) or Right (East).
It is very possible the brown door is in Room 1 (e.g., on the Left/West wall).

However, often these tasks put doors to progress.
Let's check the surroundings of `basket` and `plant` more or the `television`/`cap`.
`television` (West) and `cap` (East) are closer to the yellow door.
Maybe the brown door is near them?

Let's try to look at the other walls of Room 2.
I am at `basket` facing North.
I can Rotate to face East or South.
If I face South, I look back at the yellow door and potentially the corners I missed.
If I face East, I look at the East wall.

Alternatively, I can Jump to `cap` or `television`.
`Cap` is roughly East/South-East. `Television` is West/South-West.

Let's try jumping to the `cap`. It's near the yellow door and on the East side.
From `cap`, I can look North or East or South.
If I jump to `cap`, I should probably look East or South to see walls I haven't seen.
Or I can Jump back to `yellow door` and look into Room 1 to check for the brown door there.

Let's consider the cost. 16 steps left.
If I jump to `yellow door`, I can verify Room 1.
If I jump to `cap`, I explore Room 2 more.

Hypothesis: Brown door is in Room 1. Why? I only looked Forward in Room 1. Room 1 is the "hub" or just the start. If I missed a door in Room 1, I can't reach Room 3.
Hypothesis: Brown door is in Room 2. I haven't seen it yet.

Let's clear Room 2 first. I am deep in Room 2.
Let's Jump to `cap` (closer to entry) and Rotate to look at the East wall or South wall.
Currently at Basket (North-East). Cap is South of Basket (Front-right from door, Basket was Front-slight-right far).

Let's JumpTo(cap).
Orientation: I am facing North currently. Jump doesn't change orientation.
At `cap` (facing North), I would see Basket (North).
I want to see East or South.
Let's Rotate(90) to face East. Or 180 to face South.
If I face South at Cap, I look at the wall next to the yellow door (since Cap is near yellow door).
If I face East, I look at the side wall.

Let's try: JumpTo(cap), Rotate(90), Observe().
This checks the East wall of Room 2.

Wait, is it possible the brown door is in Room 1?
If I go back to `yellow door`, I can rotate 180 and see the rest of Room 1.

Let's assume the brown door is in Room 2 for a moment.
If I jump to `television` (West side), I can look West.

Let's try to find the brown door in Room 2.
I'll Jump to the `television` and look West.
Current pos: Basket.
Action: JumpTo(television). Rotate(-90) (since I am facing North, -90 makes me face West). Observe.

I am currently at the `basket` in Room 2. I just rotated to face North.
Observation: `plant` is front-left.
This confirms `plant` is to the West of `basket` (since I face North).
I still haven't seen the `brown door`.
I have observed `television`, `cap`, `plant`, `basket` in Room 2.
I observed `yell...

THINK:
I failed to jump to `television` because it was not in my FOV from the `basket` (facing North). I am still at the `basket` facing North. The automatic `Observe()` confirmed I can see the `plant` (front-left).

I need to construct the cognitive map based on my observations so far.
- Initial Pose: (0,0), Facing North (Room 1).
- Step 1: Observed `yellow door` at front-slight-right, mid distance (approx 2-4 units), on front wall. Let's estimate position. "Mid distance" (2, 4]. "Front wall" suggests some y > 0. Let's say (1, 3) or (2, 3).
- Step 2: Jumped to `yellow door`. Facing North.
- Observed `television` (West, near), `cap` (East, near).
- Observed `basket` (NE, slightly far), `plant` (NW, slightly far).
- Relations: `television` is West of `cap`. `cap` is South of `basket`.
- Let's assign coordinates relative to the door.
- Door at (X, Y). Facing North.
- `television`: Front-Left (West). Let's say (X-2, Y+2).
- `cap`: Front-Right (East). Let's say (X+2, Y+2).
- `plant`: Front-Slight-Left (NW). Further away. (X-2, Y+5).
- `basket`: Front-Slight-Right (NE). Further away. (X+2, Y+5).
- Distance check: "Mid" (2-4), "Slightly Far" (4-8).
- Let's refine. If door is at (1,3).
- TV roughly (-1, 5). Cap roughly (3, 5).
- Plant roughly (-1, 8). Basket roughly (3, 8).
- Relations check: TV is West of Cap? Yes (-1 vs 3). Cap is South of Basket? Yes (5 vs 8).
- Step 3: Jumped to `plant` (approx -1, 8). Rotated 90 (Facing East).
- Observed `basket` (Front-Right). Front is East. Front-Right is SE.
- My estimate for Basket was (3, 8). Plant is (-1, 8).
- From (-1, 8) facing East, (3, 8) is strictly Front.
- Observation said `basket`: Front-right. This implies Basket is South of Plant's East vector. So Basket Y < Plant Y?
- Or maybe my coordinate estimation is slightly off. Let's stick to the topological relations.
- Step 4: Jumped to `basket`. Rotated -90 (Facing North).
- Observed `plant` (Front-Left).
- From Basket (facing North), Plant is Front-Left (NW).
- This implies Plant Y > Basket Y (Front) and Plant X < Basket X (Left).
- Conflict: Previous step (Plant -> Basket, facing East) said Basket is SE. Plant -> Basket vector: (+x, -y).
- Current step (Basket -> Plant, facing North) says Plant is NW. Basket -> Plant vector: (-x, +y).
- These are consistent. Plant is North-West of Basket? No.
- If Basket is SE of Plant: Plant is NW of Basket. Yes.
- So Plant Y > Basket Y is wrong.
- Let's re-evaluate "Front-Right" from Plant (facing East).
- Facing East (1, 0).
- Front-Right is bin (22.5, 45]. Vector roughly (1, -1). SE.
- So Basket is SE of Plant. X_basket > X_plant, Y_basket < Y_plant.
- From Basket (facing North). Facing (0, 1).
- Plant is Front-Left. Bin [-45, -22.5). Vector roughly (-1, 1). NW.
- So Plant is NW of Basket. X_plant < X_basket, Y_plant > Y_basket.
- This is consistent.
- So Y_plant > Y_basket.
- X_basket > X_plant.

Let's assign coordinates for the map:
- Agent Start: (0,0), North.
- Yellow Door: (1, 3). (Mid dist, front-right).
- Jump to Yellow Door (1, 3). Facing North.
- Cap (East side): (3, 4). (Mid dist from door).
- TV (West side): (-1, 4). (Mid dist from door).
- Plant (NW side): (-1, 8). (Slightly far from door).
- Basket (NE side): (3, 7). (Slightly far from door).
- Check relations:
- Plant (-1, 8) -> Basket (3, 7). dx=4, dy=-1. Facing East from Plant. Relative (4, -1). Angle: slightly South of East. "Front-Right". Matches.
- Basket (3, 7) -> Plant (-1, 8). dx=-4, dy=1. Facing North from Basket. Relative (-4, 1). Angle: slightly West of North. "Front-Left". Matches.
- Door (1, 3) -> Plant (-1, 8). dx=-2, dy=5. North: Front-Slight-Left. Matches.
- Door (1, 3) -> Basket (3, 7). dx=2, dy=4. North: Front-Slight-Right. Matches.

Current Position: At `basket` (3, 7). Facing North.

Map should include: agent, yellow door, television, cap, basket, plant.

FINAL ANSWER:
```json
{
"agent": {"position": [3, 7], "facing": "north"},
"yellow door": {"position": [1, 3], "facing": "north"},
"television": {"position": [-1, 4], "facing": "east"},
"cap": {"position": [3, 4], "facing": "west"},
"basket": {"position": [3, 7]},
"plant": {"position": [-1, 8]}
}
```

THINK:
I failed to jump to `television` because it was not in my FOV from the `basket` (facing North). I am still at the `basket` facing North. The automatic `Observe()` confirmed I can see the `plant` (front-left).

I need to construct the cognitive map based on my observations so far.
- Initial Po...

{
  "agent": {
    "position": [
      3,
      7
    ],
    "facing": "north"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "television": {
    "position": [
      -1,
      4
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      3,
      4
    ],
    "facing": "west"
  },
  "basket": {
    "position": [
      3,
      7
    ]
  },
  "plant": {
    "position": [
      -1,
      8
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      7
    ],
    "facing": "north"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      7
    ],
    "facing": "north"
  }
}

THINK:
I attempted to jump to the `television` from the `basket`, but it failed because `television` was not visible from the `basket` with my North facing orientation. The system executed an `Observe()` instead.
My current position is still at the `basket`. My orientation is North (since the Jump failed and no rotation occurred, but wait - the previous action was `JumpTo(basket), Rotate(-90)`. I did that successfully. The *failed* action was `JumpTo(television)`).
Wait, the error message says: "Cannot jump to 'television': object not visible. Subsequent actions are skipped due to failure, instead an observe is executed: You observe: • plant: front-left, mid distance."
So I am still at `basket`, facing North.
I see `plant` to the front-left.

I need to output the **Local Cognitive Map** relative to the agent *now*.
Agent is at `basket`, facing North.
Observation:
- `plant`: front-left, mid distance.
- "front-left" corresponds to bearing approx -45 degrees.
- "mid distance" corresponds to (2, 4]. Let's say approx 3 units.
- In agent frame (+y is forward/North, +x is right/East):
- front-left is roughly (-x, +y).
- Coordinates: approx (-2, 2) or (-3, 3).
- Since I am at Basket and facing North, Plant is to my West-North.
- Previously, I went from Plant to Basket. Plant was West of Basket?
- At Plant (facing East), Basket was Front-Right (South-East).
- So Basket is East-South of Plant.
- So Plant is West-North of Basket. Matches "front-left" when facing North.
- Let's estimate local coordinates. "front-left" means roughly x < 0, y > 0.
- Distance ~3. Let's use [-2, 2].

The prompt asks for "Local Cognitive Map".
"include all objects and doors in your current field of view; exclude agent."
Only `plant` is visible.

JSON format:
origin: "agent"
objects: { "plant": { "position": [x, y] } }
(facing is not specified for plant in the observation text, so omit it).

Values:
Plant: front-left, mid-distance.
Relative position: x negative, y positive.
Let's assign [-2, 2] as a representative position for "front-left, mid distance".

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"plant": {"position": [-2, 2]}
}
}

THINK:
I attempted to jump to the `television` from the `basket`, but it failed because `television` was not visible from the `basket` with my North facing orientation. The system executed an `Observe()` instead.
My current position is still at the `basket`. My orientation is North (since the Jump f...

{
  "origin": "agent",
  "objects": {
    "plant": {
      "position": [
        -2,
        2
      ]
    }
  }
}

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

{
  "origin": "agent",
  "objects": {
    "plant": {
      "position": [
        -2,
        2
      ]
    }
  }
}

THINK:
I am the agent represented by `*` on the map.
My current position is at the `basket` (from previous turns).
I am facing North (Up).
The map shows Room 2 (the upper room) and Room 1 (the lower room).
The `+` between them is the yellow door.
I am in Room 2.
My last action failed because `television` was not visible from `basket`.
I am currently at `basket` facing North.
My field of view covers the area North of me.
The points A, B, C, G are in the southern/middle part of Room 2.
The points K, L are in the northern part of Room 2.
E, F, H, I, J, D are in Room 1.

I need to identify points in *unexplored/unobserved* regions.
"Unobserved" means areas I haven't seen yet or areas that are currently unknown.
However, the prompt asks for "candidates located in unexplored/unobserved regions".
Based on my history:
1. Room 1 (0,0) facing North: Saw yellow door (North-ish). The area behind me (South) and to sides (East/West) in Room 1 was not observed.
- Points D, E, H, J are in Room 1. F, I are also in Room 1.
- From (0,0) facing North, I saw a cone forward. The yellow door is at the boundary. I likely saw the central strip of Room 1 leading to the door.
- Points to the sides (West part of Room 1) might be unobserved. D is deep in the corner. E is West-ish.
- Points in the South of Room 1 (behind start) are definitely unobserved. J is South.
- I have not looked back in Room 1.

2. Room 2:
- Entered from yellow door facing North. Saw TV (West), Cap (East), Plant (NW), Basket (NE).
- This observed the central cone of Room 2.
- Jumped to Plant (NW), rotated to East. Saw Basket. This observed the Northern strip.
- Jumped to Basket (NE), rotated to North. Saw Plant. This observed the Northern strip again/wall.
- The corners A, C (South-West and South-East of Room 2) might be less observed?
- Actually, from the door, I saw TV (West) and Cap (East). The area immediately left/right of the door (corners) might be unobserved if the FOV is strict 90 degrees.
- L is North of me. I am looking North. I probably see L.
- K is West of me. I am looking North. K is likely out of FOV (to my left).
- A, G, B, C are South of me. I am looking North. They are definitely not currently visible.
- But have I seen them *before*?
- From yellow door facing North: I saw "television" (front-left) and "cap" (front-right). A and G are near TV. B and C are near Cap. They were likely observed or at least "swept".
- However, the question asks for "unexplored/unobserved regions".
- Usually, points behind walls or in corners not looked at are candidates.
- D, J, H, I, E, F are in Room 1. I barely looked at Room 1. I only looked forward from start.
- D (SW corner), J (South), H (Center), E (West), I (East), F (Near door).
- I likely saw F and H. I might not have seen D, J (behind/side).
- Room 1 is definitely less explored than Room 2.

- Room 2: K is near Plant. L is North wall.
- I have been to Plant. I have looked East from Plant.
- I am at Basket facing North.
- K is West.
- L is North.
- I likely observed L.

- What about A, G, B, C?
- G is West. A is West. Near TV.
- B, C are East. Near Cap.
- I saw TV and Cap.

- Let's look at the map closely.
- Room 1 (bottom) has candidates D, E, F, H, I, J.
- Start was (0,0). Let's assume (0,0) is near J or D?
- The map shows the yellow door at the top of Room 1.
- Start position (0,0) is usually bottom-left or center.
- If I started at J or below H and looked North, I saw F and the door.
- I did NOT see D (West corner) or E (West wall) or I (East wall) if FOV is 90 deg.
- So D, E, I, J are strong candidates for unobserved.

- Room 2 (top).
- I am at *.
- K, L are candidates.
- A, B, C, G are candidates.
- I am at * (Basket). Facing North.
- I see North. L is in front of me.
- K is to the left.
- A, G are SW. B, C are SE.
- I have previously stood at the door (South of A/B/C/G) looking North. I saw TV (near A/G) and Cap (near B/C). So A, G, B, C were likely in FOV.
- I stood at Plant (near K) looking East. I saw Basket (*).
- I am at Basket (*) looking North.
- Regions definitely unobserved:
- Room 1's side/back areas (D, E, I, J).
- Room 2's specific blind spots?
- From door looking North, I see a cone. Corners A/G and B/C might be visible if "mid distance" covers them.
- K (West of Basket, East of Plant). From Plant looking East, I saw Basket. K is between Plant and Basket? Or North of Plant?
- K is West of *. Plant is West of *. K is between. I likely saw K when looking East from Plant?
- But maybe not clearly.

- However, Room 1 is the most unexplored.
- D, E, H, I, J.
- Specifically, D and J are deep/behind.

- Let's selecting the clearest "unobserved" areas.
- D, J, E, I in Room 1.
- In Room 2, maybe L? (If I am at * facing North, L is North. I see it now. So it's observed).
- A, B, C, G? I saw TV and Cap.
- K? Between Plant and Basket.

- Let's assume the question implies "currently unobserved" or "never observed". Usually it means "regions you haven't mapped/seen".
- I haven't seen the West wall of Room 1 (D, E).
- I haven't seen the East wall of Room 1 (I).
- I haven't seen the South wall of Room 1 (J).
- So D, E, I, J are the best answers.

- In Room 2?
- I have been to door, Plant, Basket.
- I have seen TV, Cap, Plant, Basket.
- I have looked North (from door), East (from Plant), North (from Basket).
- I haven't looked West (from Basket) or South (from Plant/Basket).
- But looking North from door covered the South part of Room 2.
- Looking East from Plant covered the North part (Plant -> Basket).
- Looking North from Basket covers North part.
- So Room 2 is fairly well explored.
- Room 1 is the main gap.

- Let's select D, E, I, J.
- Are there others?
- A, B, C, G in Room 2.
- A is West wall. G is near A.
- B is East wall. C is near B.
- TV was "front-left" from door. Cap was "front-right".
- This implies I saw the objects. Did I see the walls behind them (A, B)? Probably.

- Let's focus on Room 1.
- D, E, F, H, I, J.
- F is in front of the door. I walked through there.
- H is in the middle.
- J is bottom.
- D is bottom-left.
- E is left.
- I is right.
- I started at (0,0) facing North.
- If (0,0) is near J, I saw H, F.
- I did NOT see D (left), E (left), I (right).
- So D, E, I, J (if start was slightly ahead of J).

Let's pick D, E, I, J.
Also maybe K (if looking East from Plant missed the area slightly South of the scan line?). No, Plant to Basket is a diagonal or straight line.

Let's stick to the obvious ones in Room 1.
And maybe A, C if the corners were tight.
But the Fog Probe usually highlights the "unknown".
Room 1 is largely unknown.
Room 2 is largely known.
So I will select points in Room 1.
D, E, I, J.
Also H? H is in the middle. I likely jumped over it or saw it.
F? I jumped to the door.

Wait, look at the map coordinates.
Start (0,0) is "bottom-left".
Room 1 is bottom. Room 2 is top.
So (0,0) corresponds to the D/J area?
If I am at (0,0) and face North:
I see a cone towards North.
If (0,0) is D, then I see E, F.
If (0,0) is J, I see H, F.
The map shows D at the far left wall. J is in the middle column bottom.
The description says: "You current (initial) position is in room 1 and you face north... origin (0, 0)".
Usually (0,0) is the bottom-left corner of the grid, or relative to the room.
If (0,0) is the bottom-left of Room 1 (point D approx?), and I face North, I see E. I might not see J (right) or I (far right).
If (0,0) is the "initial position" and denoted as origin.
But the map legend says "(0, 0) is at the bottom-left (last row, first column)".
Point D is at the bottom-left wall area.
So if I started at D, I saw the strip along the left wall (E) and maybe angled right towards the door.
But the yellow door is central.
If I started at D and the door is central, I would have to turn or see it peripherally.
However, the prompt said "yellow door: front-slight-right".
This implies I was to the left of the door.
If I was at D (left), the door (center) is front-right. This matches.
So I started near D.
I saw E (front), door (front-right).
I probably did NOT see J (right), I (far right), H (center-right).
I jumped to the yellow door.
So the right side of Room 1 (J, H, I) is unobserved.
The left side (D, E) was my start/path.

What about Room 2?
I entered yellow door. Saw TV (front-left -> West), Cap (front-right -> East).
I saw A, G (West). B, C (East).
I jumped to Plant (NW). Saw Basket (NE).
I jumped to Basket (NE). Saw Plant (NW).
Room 2 is well covered.

So the candidates are mainly in the right side of Room 1: H, I, J.
And maybe the far corners of Room 2 if the cone was narrow? But "mid distance" usually covers a lot.
However, K, L might be observed.

Wait, let's re-evaluate "Fog Probe". It asks for "unexplored/unobserved regions".
If I started at D (0,0) and saw North-East cone:
I saw the door.
I likely missed the deep right corner (I) and the bottom right (J).
I observed E? Yes, if I was at D facing North, E is North.

So I, J are definitely unobserved.
What about Room 2 "fog"?
I've been crisscrossing it.
So I'll focus on I, J.
Maybe H? H is near the path to the door.
Let's include D? No, I started there.

Let's look at the candidates again.
A, B, C, D, E, F, G, H, I, J, K, L.
My path: D (Start) -> Door (+) -> Plant (NW) -> Basket (NE).
Observed from D: E, Door.
Observed from Door: TV (near A), Cap (near B), Plant (near K), Basket (near *).
Observed from Plant: Basket.
Observed from Basket: Plant.

Unobserved areas:
- Room 1: Right side (J, I). Maybe H?
- Room 2:
- Behind objects?
- L (North wall). From Basket facing North, L is front. I see it now.
- K (West wall). From Plant facing East, I saw Basket. I didn't see K (behind me or side). From Basket facing North, K is West (left). I see "front-left: Plant". K is near Plant. I might see it.
- A, G (West/SW). From Door, I saw TV. A, G are near TV. Likely seen.
- B, C (East/SE). From Door, I saw Cap. B, C near Cap. Likely seen.

There is a possibility I missed the "brown door".
If brown door is in Room 1 (Right side), I missed it.
So I and J are critical.

What about D? I started there.
E? I walked past it.
F? Near door.

So, I will select J, I.
Also, is it possible I missed A or C?
The prompt for Fog Probe usually implies significantly unvisited areas.
I'll stick to Room 1's unvisited side.

Wait, "Select the points that are located in unexplored/unobserved regions."
Map shows:
#..E..F########
#..H.I.#......#
#..J...#......#
#D.....+......#

Wait, map layout:
Room 1 is the block on the bottom left?
No, look at the walls.
Room 1 seems to be the area enclosed by # around D, E, F, H, I, J.
Wait, look at the boundaries.
Left wall is column 0.
Right wall of Room 1 is column ~7?
Top wall of Room 1 is row ~7 (where + is).
Bottom wall is row 13?

The + (yellow door) connects Room 1 (bottom) and Room 2 (top).
Room 2 is the large area above.
Room 2 has A, G, B, C, K, L, *.
Room 1 has D, E, F, H, I, J.

If I started at D (bottom-left) and faced North.
I saw E (North).
I saw Door (North-East).
I likely saw F (Near Door).
Did I see H, I, J?
H is "East" of E. "South" of F.
J is "East" of D. "South" of H.
I is "East" of H.

FOV is 90 degrees (Front-Left to Front-Right).
If facing North from D:
Cone covers North-West to North-East?
No, North-45 to North+45.
So from D(0,0), I see (x, y) where x >= 0 and y > x (approx).
I see the diagonal D -> Door.
I see E (x=small, y=med).
I see F (x=med, y=med).
I see H (x=med, y=low)? H is (x~3, y~3). D is (0,0).
Angle to H: atan(3/3) = 45 deg. Right edge of FOV. H is visible.
Angle to J: J is (x~3, y~0)? No, J is above bottom wall.
If J is (3, 1) and D is (1, 1). Angle is 0 deg (East).
Facing North (90 deg).
J is at -90 deg relative to facing? No, 90 deg right.
FOV is +/- 45.
So I do NOT see J (East).
I do NOT see I (East-North-East).

So J and I are unobserved.
What about A, B, C?
From Door (+) facing North.
A is West. B is East.
Cone is NW to NE.
A (West) is 90 deg Left. Out of FOV?
TV was "front-left".
If TV is at A, it is visible.
"Front-left" is 0 to 45 deg left.
So TV is within 45 deg.
So A is likely visible.
Same for Cap (front-right).
So B, C are likely visible.

What about K, L?
L is North. Visible from Door?
"Mid distance" TV/Cap. "Slightly far" Plant/Basket.
L is "Very far"? Or "Slightly far"?
L is top wall.
Plant/Basket are "slightly far".
L might be further.
However, from Basket (*) facing North.
L is Front. Distance 2-4 units?
So L is visible NOW.

So the only unobserved candidates are J and I (and maybe parts of H).
I'll select J, I.
Also, look at the map for "candidates".
There are A, B, C, D, E, F, G, H, I, J, K, L.
Candidates J and I are the strongest.
Maybe D? (I started there, but technically looking North doesn't reveal the point itself? No, you know where you are).

What about the Room 3?
Is there a Room 3?
I haven't found a second door.
Usually the unexplored area contains the door.
If J and I are unexplored, the brown door might be there.
Or maybe in the unobserved corners of Room 2?
A, B, C?
If TV/Cap were visible, the corners behind them might be shadowed?
But "Fog Probe" usually points to large chunks.
I'll go with J, I.
Wait, look at the map again.
Room 1 has a right side extension?
#..H.I.#......#
#..J...#......#
The area right of I/J is "#......#".
Is that another room?
It looks like a wall separating Room 1 from a right-side area.
Is there a door in that wall?
I haven't looked at it.
So I and J are the frontier to that potential area.

My choice: J, I.
Let's check if there are others.
Unexplored = I haven't been there or seen it.
I haven't been to J or I.
I haven't seen J or I.
So J, I.

Is A unexplored? I haven't been to A. I saw TV near it.
Is B unexplored? I haven't been to B. I saw Cap near it.
Is G unexplored?
Is C unexplored?
Usually, seeing the object "Television" doesn't mean I mapped the empty space A.
But "unobserved" means strictly not in FOV.
If TV is at A, and I saw TV, I observed A.

So J, I are the best.
I'll also include D? No.

Wait, let's look at the map "Example".
It lists A, C.

I will list J, I.
Maybe A, C, G, B?
If I am cautious, I'd say the corners A and C are often missed if FOV is narrow.
But J and I are completely 90 deg off my start vector.
So J, I are definitely unobserved.

I will go with J, I.
Actually, look at E.
If I started at D and looked North. E is on the line.

Let's check if Room 3 is visible.
The map shows a third room to the right of Room 1?
The dots "......" on the right.
There is a vertical wall separating Room 1 and this area.
I need to find a door in that wall.
I haven't seen that wall (East wall of Room 1).
So I, J are the key.

One more thing: K.
K is in Room 2, West side.
From Door: Saw Plant (NW). K is near Plant.
From Plant: Saw Basket (E).
From Basket: Saw Plant (W).
K is between Plant and West wall.
I likely saw it.

Final decision: J, I.

FINAL ANSWER: { "unexplored": ["J", "I"] }

THINK:
I am the agent represented by `*` on the map.
My current position is at the `basket` (from previous turns).
I am facing North (Up).
The map shows Room 2 (the upper room) and Room 1 (the lower room).
The `+` between them is the yellow door.
I am in Room 2.
My last action failed because `televi...

###############
###...L..######
###......######
###.K..*.######
###......######
###......######
###AG..BC######
######+########
#..E..F########
#..H.I.#......#
#..J...#......#
#......#......#
#D.....+......#
#......#......#
########......#
###############

Cannot jump to 'television': object not visible. Subsequent actions are skipped due to failure, instead an observe is executed: You observe:
• plant: front-left, mid distance.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

Cannot jump to 'television': object not visible. Subsequent actions are skipped due to failure, instead an observe is executed: You observe:
• plant: front-left, mid distance.
You have a maximum of 15 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
F...

My previous action failed because `television` was not in my FOV from the `basket` (facing North).
I am currently at `basket` facing North.
Visible objects from here: `plant` (front-left).
I need to navigate to other objects. `plant` is visible.
I should jump to `plant`.
From `plant`, I can try to find the `television` or `cap`.
From `plant` (facing North, if I arrive from Basket facing North), `television` should be roughly South or South-West.
I need to look for the brown door or the other objects to navigate back or further.
Let's Jump to `plant`.
From `plant`, I want to look South to find the `television`, `cap`, and `yellow door`.
So, JumpTo(plant), Rotate(180) (to face South), Observe().
This will re-establish visual contact with the southern part of Room 2.

My previous action failed because `television` was not in my FOV from the `basket` (facing North).
I am currently at `basket` facing North.
Visible objects from here: `plant` (front-left).
I need to navigate to other objects. `plant` is visible.
I should jump to `plant`.
From `plant`, I can try to f...

THINK:
I need to update the global cognitive map based on my observations.
Initial State: Agent at (0,0) facing North.
Observation 1 (from (0,0) facing N):
- `yellow door`: front-slight-right (approx NE), mid distance (approx 3-4m), on front wall.
Let's estimate coordinates. Front is +y. Slight right is +x.
Let's say `yellow door` is at roughly (1, 3) or (2, 4).
The door connects Room 1 and Room 2. The wall is "front wall" of Room 1.
Since I jumped to `yellow door` and then into Room 2, let's fix `yellow door` at a position.
Let's assume `yellow door` is at (1, 3). Agent facing North.

Action 2: JumpTo(`yellow door`). Observe.
- I am at `yellow door` (1, 3).
- Facing North (into Room 2).
- Observed:
- `television`: front-left (NW), mid distance. Approx (-1, 5) or (-2, 6).
- `cap`: front-right (NE), mid distance. Approx (3, 5) or (4, 6).
- `basket`: front-slight-right (NNE), slightly far. Approx (2, 7) or (3, 8).
- `plant`: front-slight-left (NNW), slightly far. Approx (0, 7) or (-1, 8).
- Relations: TV West of Cap (consistent), Cap South of Basket (consistent).

Action 3: JumpTo(`plant`). Rotate 90 (Face East). Observe.
- At `plant` (approx (-1, 8)). Facing East.
- Observed: `basket` front-right.
- Facing East, front is +x. Right is -y (South). Front-right is SE.
- Basket is at (2, 7) or (3, 8). From (-1, 8), (3, 8) is pure East (Front). (2, 7) is East-South (Front-Right). Consistent.

Action 4: JumpTo(`basket`). Rotate -90 (Face North). Observe.
- At `basket` (approx (2, 7)). Facing North.
- Observed: `plant` front-left.
- Facing North, front is +y. Left is -x. Front-left is NW.
- Plant at (-1, 8) from (2, 7) is NW. Consistent.

Action 5: JumpTo(`television`) failed. Jumped to `plant` (approx (-1, 8)). Rotate 180 (Face South). Observe.
- At `plant` (-1, 8). Facing South.
- Observed:
- `television`: front (South). Mid distance.
- TV was estimated at (-1, 5). From (-1, 8) facing South, (-1, 5) is Front. Consistent.
- `cap`: front-left (South-East). Slightly far.
- Cap was estimated at (3, 5). From (-1, 8) facing South, (3, 5) is SE (Front-Left). Consistent.
- `basket`: front-left (South-East). Mid distance.
- Basket at (2, 7). From (-1, 8) facing South, (2, 7) is SE. Consistent.
- `yellow door`: front-slight-left (South-Eastish). Slightly far.
- Door at (1, 3). From (-1, 8) facing South, (1, 3) is SE. Consistent.

Coordinates refinement:
- `yellow door`: (1, 3). Facing North? It's a door. Let's not assign facing unless specified.
- `television`: West of Cap. Approx x=-2. y=5. Facing "backward" (from Plant facing South).
- "backward" relative to agent facing South means TV faces North.
- `cap`: East of TV. Approx x=2. y=5. Facing "left" (relative to agent facing South).
- Agent faces South. Left is East. So Cap faces East.
- `plant`: North of TV. Approx x=-2. y=8.
- `basket`: North of Cap. Approx x=2. y=8.
- Agent: Currently at `plant` (-2, 8). Facing South.

Let's refine distances.
- Door (1, 3) to Plant (-2, 8): dx=-3, dy=5. Dist = sqrt(9+25) = 5.8 (slightly far). Matches.
- Door (1, 3) to Basket (2, 8): dx=1, dy=5. Dist = 5.1 (slightly far). Matches.
- Door (1, 3) to TV (-2, 5): dx=-3, dy=2. Dist = 3.6 (mid). Matches.
- Door (1, 3) to Cap (2, 5): dx=1, dy=2. Dist = 2.2 (near/mid). Matches.
- Plant (-2, 8) to TV (-2, 5): dy=3. Dist 3 (mid). Matches.
- Plant (-2, 8) to Basket (2, 8): dx=4. Dist 4 (mid). Matches.
- Plant (-2, 8) to Cap (2, 5): dx=4, dy=3. Dist 5 (slightly far). Matches.
- Plant (-2, 8) to Door (1, 3): dx=3, dy=5. Dist 5.8 (slightly far). Matches.

Let's use these coordinates:
- Agent start: (0,0) N.
- Yellow Door: (1, 3).
- Television: (-2, 5). Facing North (from observation "facing backward" when looking South. Backward of South is North).
- Cap: (2, 5). Facing East (from observation "facing left" when looking South. Left of South is East).
- Plant: (-2, 8).
- Basket: (2, 8).

Agent is at Plant (-2, 8) facing South.

FINAL ANSWER:
```json
{
"agent": {"position": [-2, 8], "facing": "south"},
"yellow door": {"position": [1, 3]},
"television": {"position": [-2, 5], "facing": "north"},
"cap": {"position": [2, 5], "facing": "east"},
"basket": {"position": [2, 8]},
"plant": {"position": [-2, 8]}
}
```

THINK:
I need to update the global cognitive map based on my observations.
Initial State: Agent at (0,0) facing North.
Observation 1 (from (0,0) facing N):
- `yellow door`: front-slight-right (approx NE), mid distance (approx 3-4m), on front wall.
Let's estimate coordinates. Front is +y. Slight ri...

{
  "agent": {
    "position": [
      -2,
      8
    ],
    "facing": "south"
  },
  "yellow door": {
    "position": [
      1,
      3
    ]
  },
  "television": {
    "position": [
      -2,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      8
    ]
  },
  "plant": {
    "position": [
      -2,
      8
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      9
    ],
    "facing": "south"
  }
}

THINK:
I am at the `plant`. I just rotated 180 degrees.
My previous absolute orientation was North (when I jumped to `plant`, I didn't change orientation from `basket` where I faced North).
Then I rotated 180. So my *current* absolute orientation is South.
However, the instructions for the "Local Cognitive Map" say to use the agent's *current* position and orientation as the origin and +y axis.
So, in this local frame:
- Origin (0,0) is `plant`.
- +y is the direction I am facing (South in absolute terms).
- +x is to my right (West in absolute terms).
- -x is to my left (East in absolute terms).

Observations from current view:
- `television`: "front, mid distance, facing backward".
- "front" -> +y axis.
- "mid distance" -> let's estimate 3 units (bins: 2-4).
- "facing backward" relative to me. If I am facing South (+y), backward is North (-y). So television faces -y in local frame.
- Position: [0, 3].
- `cap`: "front-left, slightly far, facing left".
- "front-left" -> Quadrant II (+y, -x).
- "slightly far" -> let's estimate 5 or 6 units.
- "facing left" relative to me. Left is -x. So cap faces -x.
- Position: [-3, 5] approx.
- `basket`: "front-left, mid distance".
- "front-left" -> Quadrant II.
- "mid distance" -> ~3-4 units.
- Position: [-2, 3] approx.
- `yellow door`: "front-slight-left, slightly far, on front wall".
- "front-slight-left" -> +y, slightly -x.
- "slightly far" -> ~6 units.
- "on front wall" -> the wall is in front of me. The door's orientation usually faces into the room or out. If I see it, it's facing me or I am looking at it. Doors are bidirectional but often described as 'facing' the agent if visible. Or I can just omit facing if not specified as "facing X". The prompt says "on front wall". I'll assume it faces -y (towards me).
- Position: [-1, 6] approx.

Let's refine coordinates based on the "North" assumption provided in the prompt text:
"Assume your current facing direction is called 'north':"
- `television` is east (wait, the prompt text says "television is east" relative to the "north" assumption? Or is it describing the relationships?)
- The text says: "Assume your current facing direction is called 'north': television is west, near to cap" -> NO, looking at the previous turn log provided in the prompt:
"Assume your current facing direction is called 'north':
• television is east, near to cap
• cap is north, near to basket."
Wait, the prompt text above says:
"Assume your current facing direction is called 'north':
• television is east, near to cap"
But my observation says `television` is "front". If "front" is "north", then television is North.
Let's re-read the prompt carefully.
"You observe: ... Assume your current facing direction is called 'north': • television is east..."
This seems contradictory or I am misinterpreting.
"Front" is my current facing direction. If we call that "north", then "front" = "north".
Then `television` (front) should be North.
But the text says "television is east". This implies the *relative* description "television is east" might be referring to a different frame or I am misunderstanding.
Actually, maybe the text "Assume your current facing direction is called 'north'" applies to the *proximity* relations listed below it?
"• television is east, near to cap" -> This describes the relation *between* television and cap? No, "television is east" usually means "television is to the East of ...?" or "television is in the East direction"?
Usually, standard relations are "A is [dir] of B". Here it says "television is east, near to cap". This might mean "television is to the east (of the agent?)" but that contradicts "front".
OR, maybe "television is east" means "In the frame where 'front' is North, television is at coordinates that correspond to East". But it is "front".

Let's look at the standard observed list first: "television: front".
"front" means along the +y axis in local frame.
I will stick to the "You observe" bullet points for position.
"front" -> (0, y).
"front-left" -> (-x, y).
"front-slight-left" -> (-x small, y large).

Distances:
Mid: ~3.
Slightly far: ~5.

Positions:
TV: [0, 3]. Facing: "facing backward" -> -y.
Cap: [-3, 4] (front-left, slightly far). Facing: "facing left" -> -x.
Basket: [-2, 3] (front-left, mid).
Yellow Door: [-1, 5] (front-slight-left, slightly far).

Let's convert "facing backward" (relative to agent facing) to local axes.
Agent faces +y. Backward is -y. So TV faces -y.
Agent faces +y. Left is -x. Cap faces -x.

JSON construction:
Origin: "agent".
Objects:
- television: pos [0, 3], facing "-y"
- cap: pos [-3, 5], facing "-x"
- basket: pos [-2, 3]
- yellow door: pos [-1, 5]

(I will omit facing for basket and door as they weren't explicitly described with "facing ..." in the observation bullet points, except "on front wall" for door, which implies location/orientation, but "facing" attribute is specifically for objects like TV/Cap/Chair. The prompt says "Include only observed objects... MUST include facing key if the object has facing direction". The door has "on front wall", maybe I should treat it as facing -y? But it's a door. I'll stick to explicit facings).
Actually, for the door, "on front wall" means the wall is perpendicular to my view. The door faces me. So "-y". I'll add it if unsure, but standard objects usually get the facing.

Re-checking the "Assume..." text.
"television is east, near to cap". If I am facing South, and TV is South of me. "East" is to my Left.
Maybe the "Assume..." text is reporting the *Cardinal* bins in a frame where my facing is North.
If I face North (hypothetically), then Front is North. TV is Front. So TV is North.
Why does it say "television is east"?
Maybe the "Assume..." block describes the *allocentric* relations if the agent was facing North?
But I am facing South (in reality).
If I ignore the "Assume..." block and trust "You observe: television: front", that is direct.

Let's trust "television: front".

Local Map:
Agent at (0,0), facing +y.
TV at (0, 3), facing -y.
Cap at (-4, 4), facing -x.
Basket at (-3, 3).
Yellow door at (-1, 5).

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"television": {"position": [0, 3], "facing": "-y"},
"cap": {"position": [-4, 5], "facing": "-x"},
"basket": {"position": [-3, 3]},
"yellow door": {"position": [-2, 6]}
}
}

THINK:
I am at the `plant`. I just rotated 180 degrees.
My previous absolute orientation was North (when I jumped to `plant`, I didn't change orientation from `basket` where I faced North).
Then I rotated 180. So my *current* absolute orientation is South.
However, the instructions for the "Local Co...

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        0,
        3
      ],
      "facing": "-y"
    },
    "cap": {
      "position": [
        -4,
        5
      ],
      "facing": "-x"
    },
    "basket": {
      "position": [
        -3,
        3
      ]
    },
    "yellow door": {
      "position": [
        -2,
        6
      ]
    }
  }
}

{
  "cap": {
    "position": [
      -2,
      4
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      -1,
      6
    ],
    "facing": "north"
  },
  "basket": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      4
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "television": {
      "position": [
        0,
        3
      ],
      "facing": "-y"
    },
    "cap": {
      "position": [
        -4,
        5
      ],
      "facing": "-x"
    },
    "basket": {
      "position": [
        -3,
        3
      ]
    },
    "yellow door": {
      "position": [
        -2,
        6
      ]
    }
  }
}

THINK:
The map shows my current position `*` in the top room (Room 2). The yellow door `+` connects this room to the room below (Room 1).
My current coordinates are relative to the start in Room 1 (which was 0,0).
Room 2 is "North" of Room 1 based on the map layout (North is Up).
I am at `plant` in Room 2.
The points A, B, C, D, E, F are in Room 1 (the bottom room).
I have only observed Room 1 from the starting position (0,0) facing North, seeing the yellow door.
I have not explored the rest of Room 1.
Points A, B, C, D, E, F are distributed in Room 1.
Since I only looked North from (0,0) and then jumped to the door, most of Room 1 is unexplored, especially the sides and back if I started in the middle.
Wait, let's re-read the start.
"You current (initial) position is in room 1 and you face north... origin (0, 0)".
I observed "yellow door: front-slight-right, mid distance, on front wall".
Then I jumped to yellow door.
So I have seen the cone towards the yellow door.
The map shows the yellow door on the top wall of the bottom room.
I am now in the top room.
The points A, B, C, D, E, F are in the bottom room.
The points A is near the top-left of the bottom room.
B is central/top.
E is near the top-right.
C is central/bottom.
D is near the bottom-right (near a door?). Wait, there is a `+` near D?
Let's look at the map closely.
Bottom room has a `+` on the top wall (yellow door).
And there is another `+` on the Right wall near D? No, the `+` near D is on the vertical wall separating the bottom-left area from... wait.
The map structure:
Top room: `*` (Agent at Plant).
Middle connection: `+` (Yellow door).
Bottom room contains A, B, C, D, E, F.
There is a `+` symbol at the coordinates near D? It looks like `#..C..D+......#`.
Yes, there is a door on the East wall of the bottom room, next to D.
This must be the brown door!
And there is a space to the right of it (Room 3?).
I have not seen this area. I only looked North from (0,0).
(0,0) is likely near C or below B.
If I looked North from (0,0) and saw the yellow door (North wall), I saw the path from (0,0) to the yellow door.
Area A (West of path) is likely unobserved.
Area B (on path?) might be observed.
Area E (East of path) might be unobserved.
Area F (West wall) unobserved.
Area C (Start area?) observed?
Area D (East wall near brown door) unobserved.
However, the prompt asks for "unexplored/unobserved regions".
Since I only did *one* observation in Room 1 (facing North), the "cone" covers the center-ish.
A, F (West side) are likely unobserved.
E, D (East side) are likely unobserved.
B might be in the cone.
C is the origin? Or near it.
Usually, "unexplored" means areas I haven't mapped or seen objects in.
Given the task is to select points in unobserved regions:
A, F, D, E are definitely candidates.
B is close to the line of sight to the door.
C is the start.
I'll select the ones that represent the "sides" and "corners" I haven't seen. A, B, C, D, E, F are all in Room 1.
I'll mark all of them as potential unexplored areas because I've left Room 1 very quickly.
Actually, looking at the map provided in the prompt:
The `+` near D suggests a door I haven't seen.
The regions A, B, C, D, E, F are all in Room 1.
I'll select all of them or the subset that is definitely off-limits from the first observation.
My first observation: "yellow door: front-slight-right...".
FOV is 90 deg.
If I am at (0,0) facing North. Cone is NW to NE (-45 to +45).
Yellow door is at (x, y). "front-slight-right" means angle is (0, 22.5].
So the door is slightly East of North.
So I see a cone slightly shifted? No, I face North. My cone is North. The object is in the right half of the cone.
So I see mostly North.
A (West/Left) might be outside FOV if it's far left.
E (East/Right) might be outside FOV if it's far right.
F (West) definitely outside.
D (East) definitely outside.
B (Central) likely inside.
C (Central/Start) is where I was.
So unexplored: A, D, E, F. Maybe B?
Let's select A, C, D, E, F. (C is near start but maybe behind me? No I was at C).
Actually, if I am at C (0,0), I observe *from* C. C is not "unobserved", it's visited.
So C is not unexplored.
B is in front. Likely observed.
A is left. Unobserved.
F is left. Unobserved.
E is right. Unobserved.
D is right. Unobserved.

So: A, D, E, F.

Wait, looking at the map again:
`#..C..D+......#`
The `+` is on the wall.
This confirms there is a door there.
I need to go back to Room 1 to see it.

Final selection: A, B, C, D, E, F.
Wait, I should only select "points located in unexplored/unobserved regions".
Room 1 is largely unexplored.
I will select A, B, D, E, F. (C is my start point, so I "know" it, but maybe I didn't observe the ground there? I observed *from* there. The region *around* C might be unobserved if I didn't look down/sides. But I was there).
Let's stick to the ones clearly off-path.
A, D, E, F.
B is between start and door, likely seen.
I will verify the list.
A: West side. Unseen.
B: Center. Seen?
C: Start. Seen.
D: East side near door. Unseen.
E: East side. Unseen.
F: West side. Unseen.

Let's refine. The prompt asks to select points.
I'll select A, B, D, E, F. I am not sure about B, but better safe.
Actually, let's look at the symbols.
A, B, E are in the upper part of Room 1.
F, C, D are in the lower part.
I started at C (approx).
I looked North.
I saw the yellow door (North wall).
So I saw the corridor from C to Door.
B is likely in that corridor.
A (Left), E (Right) are likely unseen.
F (Left), D (Right) are likely unseen.
So A, D, E, F.

Let's check the map again.
The map shows Room 1 (bottom), Room 2 (top), Room 3 (right of bottom).
The `+` near D is the door to Room 3.
I need to go there.
The points are A, B, C, D, E, F.
I'll select A, C, D, E, F.
Actually, if C is (0,0), I was there.
I'll just list the ones in the unobserved areas.
Unobserved: A, D, E, F.
I'll include B to be thorough? No, minimal set is better?
"Select the points that are located in unexplored/unobserved regions."
I'll go with A, B, C, D, E, F to indicate the room needs exploration.
But being precise: A, D, E, F.
Let's add B? No.
Let's add C? No.
Final guess: A, B, C, D, E, F.
Actually, looking at the visual mask...
I'll select A, B, C, D, E, F.
Wait, if I select C, I am saying where I started is unobserved. That's technically true for the *objects* there if I didn't look down? No, I occupy it.
I'll exclude C.
Exclude B (path).
Result: A, D, E, F.
Let's try to include all Room 1 points since I left it immediately.
Final answer logic: Room 1 is basically unexplored.
The map shows A, B, C, D, E, F in Room 1.
I will return A, B, C, D, E, F.

Wait, looking at the example `{"unexplored": ["A", "C"]}`.
I will provide the list.

Let's reconsider B. B is near the center. If I look North, I see B.
So B is observed.
C is start. Known.
So A, D, E, F.
Wait, E is near the wall. D is near the door.
F is near the wall.
A is near the wall.
I'll go with A, D, E, F.
Wait, B is "..."?
Actually, let's look at the ASCII carefully.
A is left.
B is center.
E is right.
F is left (lower).
C is center (lower).
D is right (lower).
I started at C? The map shows `*` in the top room.
My start was Room 1.
If C is the start, I saw B and the door.
So A, D, E, F are the unobserved ones.
I'll select A, D, E, F.

Wait, is C unobserved? I started there, but did I "Observe" it? `Observe()` reports objects in FOV. If I am at C, I don't see C. I see things *from* C. So C is not in the FOV.
So C might be considered "unobserved" in terms of "is there an object at C?".
However, usually "unexplored" implies areas not covered by the sensor.
Since I haven't looked at C (I looked away from it), C is unobserved.
So A, C, D, E, F.
B is observed.
Let's go with A, C, D, E, F.

Re-evaluating B.
"yellow door: front-slight-right".
The door is at the top.
B is in the middle.
It's likely B was in the FOV.
So I will exclude B.

So: A, C, D, E, F.

One more check.
Is D in FOV? "front-slight-right" might cover D if D is close to the line?
D is in the bottom-right corner.
My view is narrow (90 deg).
Line to door is roughly North.
D is East.
Angle to D is 90 deg?
If D is (x, 0) and I am (0,0) facing (0,1).
D is right (90 deg).
FOV is +/- 45 deg.
So D is outside FOV.
E is top-right.
Angle to E?
If E is (x, y) and door is (0, y).
E is East of door.
So angle is > 0.
"front-slight-right" is (0, 22.5].
So the door is nearly North.
E is further East. Angle > 22.5?
Probably. E is likely outside or on the edge.
I'll assume E is unobserved.
So A, C, D, E, F.

Final check on C.
If I stand at C, I know C is empty (except me).
So C is "explored".
I'll remove C.
So A, D, E, F.

Wait, looking at the map again.
`#..C..D+......#`
C is at the bottom.
The start position is (0,0).
(0,0) is usually bottom-left or center-bottom.
If C is (0,0), then D is (x, 0).
A is (0, y)?
Let's select all points in Room 1 except the path to the door.
Path is C -> B -> Door.
So A, D, E, F.

One detail: The prompt map has `+` near D.
This confirms D is near a door.
I definitely need to go there.

I will output A, D, E, F.
Maybe B is also unobserved if the room is wide?
I'll stick to A, D, E, F.

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

THINK:
The map shows my current position `*` in the top room (Room 2). The yellow door `+` connects this room to the room below (Room 1).
My current coordinates are relative to the start in Room 1 (which was 0,0).
Room 2 is "North" of Room 1 based on the map layout (North is Up).
I am at `plant` in ...

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

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

I am at the `plant`, facing "South" (relative to the room's North, so actually facing the door/entry side).
I see:
- `television`: front
- `cap`: front-left
- `basket`: front-left
- `yellow door`: front-slight-left

I still haven't found the `brown door`.
I have viewed Room 2 from:
1. `yellow door` facing North (Entry).
2. `plant` facing East (Side).
3. `basket` facing North (Back).
4. `plant` facing South (Front).

I have NOT viewed:
- West wall of Room 2 (from `television`?).
- East wall of Room 2 (from `cap` or `basket`?).
- Room 1 fully (only saw yellow door).

The `brown door` could be on the West wall of Room 2 (near television) or East wall (near cap/basket).
Or in Room 1.

Given `television` is "front" from `plant` (facing South), it's on the West side of the room (consistent with previous observations).
Let's go to `television` and check the West wall. If the brown door is there, I'll see it.
Action: JumpTo(television).
At `television`, I will be facing South (unchanged).
To look at the West wall, I need to rotate 90 degrees clockwise (South -> West).
Action: JumpTo(television), Rotate(90), Observe().

I am at the `plant`, facing "South" (relative to the room's North, so actually facing the door/entry side).
I see:
- `television`: front
- `cap`: front-left
- `basket`: front-left
- `yellow door`: front-slight-left

I still haven't found the `brown door`.
I have viewed Room 2 from:
1. `yellow door` ...

THINK:
I need to construct a cognitive map based on my observations.
Initial State: Room 1, (0,0), facing North.
Step 1: Observe() -> `yellow door` at front-slight-right, mid distance.
Let's approximate coordinates. "Mid distance" is (2, 4]. Let's say distance 3 or 4.
Angle front-slight-right (0 to 22.5 deg).
Let's place `yellow door` at roughly (1, 3) or (1, 4).
Let's assume `yellow door` is at (1, 4).
Step 2: JumpTo(yellow door). Position (1, 4). Facing North.
Observed:
- `television`: front-left, mid distance (~3m), facing forward. "Forward" means facing South (since I face North). Pos: (~-1, 7).
- `cap`: front-right, mid distance (~3m), facing right. "Right" means facing East? Or West? "Facing right" usually means its front is to the right. If I am facing North, right is East. So Cap faces East. Pos: (~3, 7).
- `basket`: front-slight-right, slightly far (~5m). Pos: (~3, 9).
- `plant`: front-slight-left, slightly far (~5m). Pos: (~-1, 9).

Note: The prompt gave relative relations: "television is west, near to cap", "cap is south, near to basket".
This implies a layout:
TV (West) -- Cap (East)
|
Plant (West) -- Basket (East)
Wait, "cap is south, near to basket". This means Basket is North of Cap.
So:
North
^
| Plant Basket
|
| TV Cap
|
| Door

Step 3: JumpTo(plant) at (~-1, 9). Rotate 90 (Face East).
Observed `basket` at front-right. From Plant (facing East), Front-Right is South-East.
Wait, if Plant is (-1, 9) and Basket is (3, 9), Basket is East. From Plant facing East, Basket should be Front.
Observation says "front-right". This implies Basket is South of the East vector. So maybe Basket is at (3, 7)?
But "cap is south, near to basket". If Cap is (3, 7), Basket must be North of (3, 7), e.g., (3, 9).
Let's re-read carefully: "cap is south, near to basket". This means Cap is South OF Basket. Basket is North of Cap. Correct.
Why did "front-right" appear from Plant (facing East) to Basket?
Maybe Plant is at (-1, 10) and Basket is at (3, 9)?
Vector Plant->Basket = (4, -1). Facing East (1, 0). Angle is negative (Right). Matches "front-right".
Let's refine coordinates:
Yellow Door: (1, 4).
TV: (-2, 6).
Cap: (4, 6).
Plant: (-2, 9).
Basket: (4, 9).

Step 4: JumpTo(basket) at (4, 9). Rotate -90 (Face North).
Observed `plant` front-left.
From Basket (4, 9) facing North. Plant (-2, 9) is West. Front-Left is correct.

Step 5: JumpTo(television). Failed. Not visible.
Wait, from Basket (4, 9) facing North, TV (-2, 6) is South-West. Beyond FOV (90 deg, front cone). Correct.
Observation triggered from Basket facing North: Plant front-left.

Step 6: JumpTo(plant) at (-2, 9). Rotate 180 (Face South).
Observed:
- `television`: front. (South of Plant). Consistent.
- `cap`: front-left. (South-East of Plant). Consistent.
- `basket`: front-left. (East of Plant). Consistent? Facing South, Left is East. Front-Left is South-East.
- Wait, Basket is at (4, 9). Plant is (-2, 9). Vector Plant->Basket is (6, 0) East.
- From Plant facing South, East is Left (90 deg). "Front-Left" is [0, 90]. 90 is on the border or "left". "Front-Left" bin is [-45, 0) in ego?
- Bins: 0 is front. + is right. - is left.
- Facing South (180). Basket (East) is -90 deg relative (Left).
- Usually "front-left" is [-45, 0). Left is [-90, -45)?
- The bins: [-45, -22.5) -> front-left.
- If Basket is exactly East, relative angle is 90 deg left. That's "Left", not "Front-Left".
- Maybe Basket is South-East of Plant? i.e., Basket y < Plant y.
- Previous: "cap is south, near to basket". Basket is North of Cap.
- Let's assume Plant y > Basket y.
- e.g. Plant (-2, 10), Basket (4, 9).
- From Plant (Face South): Basket is South-East. Angle left. Fits Front-Left.
- `yellow door`: front-slight-left. (South-East of Plant).
- Door at (1, 4). Plant (-2, 10). Vector (3, -6). South-East. Fits.

Step 7: JumpTo(television) at (-2, 6). Rotate 90 (Face West).
Observed: No objects.
This means West of TV is empty or wall.

Current Agent Position: `television` at approx (-2, 6).
Facing: West.

Objects:
- yellow door: (1, 4).
- television: (-2, 6). Facing South? (Obs 2: "facing forward" when agent faced North -> TV faces South).
- cap: (4, 6). Facing East? (Obs 2: "facing right" when agent faced North -> Cap faces East).
- basket: (4, 9).
- plant: (-2, 10).
- brown door: Unknown.

Let's generate the JSON.
Agent: at `television`.
Facing: "west".

FINAL ANSWER:
{
"agent": {"position": [-2, 6], "facing": "west"},
"yellow door": {"position": [1, 4], "facing": "north"},
"television": {"position": [-2, 6], "facing": "south"},
"cap": {"position": [4, 6], "facing": "east"},
"basket": {"position": [4, 9]},
"plant": {"position": [-2, 10]}
}

THINK:
I need to construct a cognitive map based on my observations.
Initial State: Room 1, (0,0), facing North.
Step 1: Observe() -> `yellow door` at front-slight-right, mid distance.
Let's approximate coordinates. "Mid distance" is (2, 4]. Let's say distance 3 or 4.
Angle front-slight-right (0 to ...

{
  "agent": {
    "position": [
      -2,
      6
    ],
    "facing": "west"
  },
  "yellow door": {
    "position": [
      1,
      4
    ],
    "facing": "north"
  },
  "television": {
    "position": [
      -2,
      6
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      4,
      6
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      4,
      9
    ]
  },
  "plant": {
    "position": [
      -2,
      10
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      5
    ],
    "facing": "west"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      5
    ],
    "facing": "west"
  }
}

THINK:
I am currently at the `television`. I just rotated 90 degrees clockwise.
Previous orientation at `plant` was South (facing the entry).
I jumped to `television` (which was "front" from `plant`, so South of `plant`).
Orientation remained South.
Then I rotated 90 degrees clockwise. South + 90 deg (clockwise) = West.
So I am now facing West.
The observation is "No objects in field of view".
This means the West wall of Room 2 is empty (or at least contains no observed objects/doors within range).

I need to construct the Local Cognitive Map.
Since there are no objects in my field of view, the "objects" dictionary will be empty.
The origin is the agent.
Facing is West (global), but local map is relative to agent (+y is forward).
So relative to me, everything is empty.

Wait, I need to be careful. The prompt asks for the map *now*, after the observation.
The observation was "No objects in field of view".
So the map is empty.

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

THINK:
I am currently at the `television`. I just rotated 90 degrees clockwise.
Previous orientation at `plant` was South (facing the entry).
I jumped to `television` (which was "front" from `plant`, so South of `plant`).
Orientation remained South.
Then I rotated 90 degrees clockwise. South + 90 de...

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

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

THINK:
I am at the `television` in Room 2, facing West. I observed "No objects". This implies I am looking at a wall or empty space.
I entered Room 2 via the yellow door (North wall of Room 1, South wall of Room 2).
Room 2 seems to be the upper room in the map.
Room 1 is the lower room.
I am currently at `television` (denoted by `*` in the map, presumably). The map shows `*` in the upper room.
The yellow door is `+` between the two rooms.
Candidates:
A: In Room 1, far left (West).
B: In Room 1, far right (East).
C: In Room 1, middle-ish.
D: In Room 1, middle.
E: In Room 1, left side.
F: In Room 1, right side.

Wait, looking at the map provided:
The agent `*` is in the upper room (Room 2).
The yellow door `+` connects the upper room and lower room.
There is another `+` in the lower room (Room 1) on the right wall? No, the map shows a `+` on the wall between the left room and right room?
Let's analyze the ASCII map.
Top block: Room 2. `*` is there.
Bottom block: Room 1.
There is a connection between Top and Bottom.
There is a label `+` at the connection.
In Room 1 (bottom), there are labels A, B, C, D, E, F.
Wait, let's look closer at the bottom part.
```
######+######## <- Door between Room 2 (top) and Room 1 (bottom)
#....CB######## <- Top of Room 1
#..E...#......#
#....D.#......#
#.....F#......#
#A.....+......# <- Another door `+` on the right wall of the left section?
#......#......#
########......#
```
The bottom structure looks like two vertical corridors or rooms side-by-side?
Actually, the '#' line `#..E...#......#` suggests a wall splitting the bottom area into left and right.
And there is a `+` in that wall? `#A.....+......#`.
So Room 1 (where I started) is likely the bottom-left room.
I started at (0,0).
If I am in Room 2 (top), and I missed the brown door.
The brown door is likely the `+` connecting the bottom-left room to the bottom-right room (or somewhere else).
The candidates A-F are in the bottom area.
A is in the bottom-left room (West).
B, C are near the door to Room 2.
D, E, F are in the bottom-left room.
Wait, let's re-read the map.
The wall separating the bottom-left and bottom-right areas has a `+`.
This suggests there is a door there.
I started in Room 1. I only saw the yellow door.
Did I miss the brown door? Yes.
The brown door is likely the one connecting Room 1 to the other room (Room 3?).
So candidates in the unexplored regions would be the ones in the bottom-right room (if any) or areas of Room 1 I haven't seen.
However, the candidates A, B, C, D, E, F are all in the bottom-left room (except maybe the right side if it's open?).
The map shows `#` between the left and right bottom parts, with a `+`.
The candidates are:
A: Bottom-left corner.
B: Top-right corner of the left room.
C: Top-center of the left room.
D: Center of the left room.
E: Mid-left of the left room.
F: Mid-right of the left room.
All A-F seem to be in Room 1 (the one I started in).
I only observed North in Room 1. I missed West, East, South.
A is West/South-West. Unexplored.
E is West. Unexplored.
D is Center (maybe seen?).
F is East. Unexplored.
B, C are near the yellow door. I might have seen them or the area.
However, I haven't observed facing South or West in Room 1.
So A, E, F are definitely unobserved.
What about B, C? They are near the North wall. I saw the yellow door there.
What about the room to the right? There are no candidates there.
The question asks to select points in unexplored/unobserved regions.
Since I only looked North from (0,0), I saw the cone towards the yellow door.
(0,0) is likely near the bottom center or bottom left.
If (0,0) is bottom-left, North is Up.
I saw the yellow door (North).
A is to the West/Left. Unexplored? If I am at (0,0) and look North, FOV is 90 deg (NW to NE).
If I am at (0,0), A (West) is outside FOV.
E (West-North) might be on the edge.
D (Center) probably seen.
C, B (North) probably seen.
F (East) might be outside FOV.
Actually, I don't know my exact starting coordinates in the room, just (0,0).
Let's assume A, E, F are the best candidates for unexplored areas in Room 1.
But wait, the map shows a `+` on the right wall of the room containing A-F. That is likely the brown door. I haven't seen it.
The candidates are locations.
I should select points that I haven't confirmed/observed.
I haven't observed A, E, F, D?
Let's stick to the most obvious ones. A (corner), E (side), F (near the other door?).
Actually, looking at the ASCII, the region on the right (bottom-right) has no labels.
So I must evaluate A-F in Room 1.
I only saw the "front" (North).
So "behind" (South) and "sides" (East/West) are unobserved.
If (0,0) is `A`? No, A is a candidate.
Usually start is centered or near a door.
If I started at (0,0) and saw yellow door mid-distance.
Yellow door is at the top.
So I was likely at the bottom.
The area "behind" me or to the "sides" is unobserved.
If I faced North, I saw a cone.
Corners A (bottom left), F (mid right), E (mid left) might be missed.
C, B are near the door, likely seen.
D is in the middle, likely seen.
So A, E, F.

Wait, is B in the unexplored set? It's in the corner. Might be occluded or outside cone.
But A, E, F are stronger candidates.
Let's look at the "Fog Probe" instructions. "Select the points that are located in unexplored/unobserved regions."
I've been in Room 2 (top).
I've been in Room 1 (bottom) only at start.
I haven't verified the brown door location.
The map shows it at the East wall of Room 1.
F is near it.
I haven't seen F.
I haven't seen A.
I haven't seen E.
I probably saw C and D. B is doubtful.
Let's verify the query. It asks for a list of strings.
I will select A, E, F, and maybe B.
Let's refine. I saw "Yellow door: front-slight-right".
This implies I was to the left of the door.
So I was on the left side of Room 1.
My cone covered the door (North-East-ish).
So I saw the center-right-top.
I missed the Left (West) and Bottom (South).
A is West/Bottom. Unexplored.
E is West. Unexplored.
F is East. If I was on the left, looking North-East (towards door), I might have seen F?
Yellow door was "front-slight-right".
My FOV is 90 (-45 to +45 relative to facing).
If door is at angle ~20 deg.
F is on the East wall. Angle to F might be > 45?
It's safer to mark F as unexplored.
And the map shows a door near F. I definitely haven't seen that door.
So F is unobserved.
A, E are on the West. Unobserved.
B is Top-Right. If door is Top-Center, B is to the right of door. I might have seen it.
C is Top-Center. Seen.
D is Center. Seen.
So A, E, F seem correct.

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

THINK:
I am at the `television` in Room 2, facing West. I observed "No objects". This implies I am looking at a wall or empty space.
I entered Room 2 via the yellow door (North wall of Room 1, South wall of Room 2).
Room 2 seems to be the upper room in the map.
Room 1 is the lower room.
I am current...

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

You jumped to television. You rotated clockwise 90°. You observe: No objects in field of view..
You have a maximum of 13 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You jumped to television. You rotated clockwise 90°. You observe: No objects in field of view..
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 `television` facing West (South + 90 deg).
I see nothing. This implies the West wall of Room 2 has no objects or doors in my FOV.
So the `brown door` is likely not on the West wall of Room 2.

Possibilities for `brown door`:
1. East wall of Room 2.
2. North wall of Room 2 (I faced North from Basket, but field of view is 90 deg, maybe I missed corners).
3. Room 1 (I haven't explored it).

Let's check the East wall of Room 2. I should go to `cap` or `basket`.
From `television` (facing West), I can't see `cap` or `basket` (they are behind me).
I need to Rotate to see them.
Rotate(-180) or Rotate(180) to face East.
Then JumpTo(`cap`).
Then Rotate to look at the East wall (if I am at Cap facing East).
Or I can just Observe from Television facing East to see if the door is visible on the far wall? Unlikely if it's a door on the wall.

Let's do this efficiently.
I am at `television` facing West.
1. Rotate(180) to face East. Observe().
This will show me `cap`, `basket`, `yellow door` (maybe), and potentially the `brown door` if it's on the East wall.

Let's try that.

I am at the `television` facing West (South + 90 deg).
I see nothing. This implies the West wall of Room 2 has no objects or doors in my FOV.
So the `brown door` is likely not on the West wall of Room 2.

Possibilities for `brown door`:
1. East wall of Room 2.
2. North wall of Room 2 (I faced North ...

THINK:
I need to construct the cognitive map based on my observations.
Initial position: (0,0), facing North.
Observation 1 (from 0,0, N): `yellow door` at front-slight-right, mid distance, on front wall.
Let's estimate coordinates. "Front wall" implies a wall at some Y. "Mid distance" is (2, 4]. Let's assume Y=3 or 4. "Front-slight-right" means slight positive X. Let's say yellow door is at (1, 3). Since it connects rooms, it's on a wall.

Jumped to `yellow door`. Facing North (unchanged).
Observation 2 (from yellow door, N):
- `television`: front-left, mid distance. (West-ish).
- `cap`: front-right, mid distance. (East-ish).
- `basket`: front-slight-right, slightly far. (Further East/North).
- `plant`: front-slight-left, slightly far. (Further West/North).
Facing of objects: TV facing forward (South?), Cap facing right (West? No, cap facing right relative to me? Or absolute? The text says "facing right". If relative to agent facing N, right is East. If absolute, it's usually cardinal. Let's assume relative to agent unless specified).
Let's place Room 2 relative to yellow door (1, 3).
Agent at (1, 3).
TV: Front-left. Maybe (-2, 5).
Cap: Front-right. Maybe (4, 5).
Plant: Front-slight-left, slightly far. Maybe (-1, 7).
Basket: Front-slight-right, slightly far. Maybe (3, 7).

Jumped to `plant`. Rotated 90 deg clockwise (Facing East).
Observation 3 (from Plant, E): `basket`: front-right, mid distance.
If Plant is at (-1, 7) and I face East. Front-Right is South-East.
Basket at (3, 7) relative to Plant (-1, 7) is East (Front).
Wait, observed "front-right". That means South-East.
My coordinates might need adjustment.
If Plant is (-2, 7) and Basket is (2, 5)?
From Door (1, 3) N:
- Plant (-2, 7) is Front-Left (dx=-3, dy=4). Angle: atan(-3/4) = -37 deg. "Front-Left" is [-45, -22.5). Fits.
- Basket (2, 5) is Front-Right (dx=1, dy=2). Angle: atan(1/2) = 26 deg. "Front-Right" is (22.5, 45). Fits.
From Plant (-2, 7) Facing East:
- Basket (2, 5) is dx=4, dy=-2. Relative to East: Front is +x. Right is -y.
dx=4 (Front), dy=-2 (Right). "Front-Right". Fits.

Jumped to `basket`. Rotated -90 (Facing North).
Observation 4 (from Basket, N): `plant`: front-left, mid distance.
From Basket (2, 5) facing N:
Plant (-2, 7) is dx=-4, dy=2.
Relative to N: Front is +y, Left is -x.
dx=-4 (Left), dy=2 (Front).
Angle relative to N: atan(-4/2) = -63 deg.
"Front-Left" is [-45, -22.5). This is "Left" or "Front-Left" boundary?
Actually, "Front-Left" is [-45, -22.5). -63 is outside, it's "Left".
The observation said "front-left".
So my Y difference must be larger or X difference smaller.
Maybe Plant (-1, 8) and Basket (2, 6)?
Door (1, 3).
Plant (-1, 8): dx=-2, dy=5. atan(-0.4) = -21. Front-slight-left. (Fits Obs 2).
Basket (2, 6): dx=1, dy=3. atan(0.33) = 18. Front-slight-right. (Fits Obs 2).
From Plant (-1, 8) facing E:
Basket (2, 6). dx=3, dy=-2. Front=3, Right=2. Angle=atan(2/3)=33 deg right. Front-Right. (Fits Obs 3).
From Basket (2, 6) facing N:
Plant (-1, 8). dx=-3, dy=2. Front=2, Left=3. Angle=atan(-3/2)=-56 deg. Still "Left" rather than "Front-Left".
Maybe Basket is further North?
If Basket (2, 8) and Plant (-1, 8)?
From Plant (-1, 8) facing E: Basket (2, 8) is Straight Front. Obs 3 said "front-right". So Basket must be South of Plant.
So Plant Y > Basket Y.
Let's try Plant (-1, 9), Basket (2, 7).
From Door (1, 3):
Plant (-1, 9): dx=-2, dy=6. Front-slight-left.
Basket (2, 7): dx=1, dy=4. Front-slight-right.
From Plant (-1, 9) E: Basket (2, 7). dx=3, dy=-2. Front-Right.
From Basket (2, 7) N: Plant (-1, 9). dx=-3, dy=2. Front-Left? Angle -56. Still wide.
Maybe distance "mid" allows for closer X?
Let's assume coordinates roughly.

Jumped to `plant`. Rotated 180 (Facing South).
Observation:
TV: Front.
Cap: Front-left.
Basket: Front-left.
Door: Front-slight-left.
From Plant (-1, 9) facing S:
TV must be South. Let's say TV (-1, 5).
Cap must be South-East (Front-Left relative to S). Say Cap (3, 5).
Basket (2, 7) relative to Plant (-1, 9) is South-East. Front-Left.
Door (1, 3) relative to Plant (-1, 9) is South-East. Front-Left? dx=2, dy=-6.
Relative to South (facing -y): Front is -y. Left is +x.
dx=2 (Left), dy=-6 (Front). Angle atan(2/6) = 18 deg. Front-slight-left. Fits.

Jumped to `television`. Rotated 90 (Facing West). Saw Nothing.
TV is at (-1, 5).

Rotated 180 (Facing East).
Observation:
Cap: Front, near.
Basket: Front-left.
From TV (-1, 5) Facing East:
Cap (3, 5) is Front (dx=4, dy=0).
Basket (2, 7) is Front-Left (dx=3, dy=2). Front is +x, Left is +y.
dx=3, dy=2. Angle atan(2/3) = 33 deg Left. Front-Left. Fits.

Current Agent Position: At `television` (-1, 5). Facing East.
Missing: Brown door.
I've checked:
- South wall of Room 2 (entry).
- West wall of Room 2 (nothing).
- North wall area (Basket/Plant seem to be objects, no door mentioned behind them, but I looked North from Basket and saw Plant. Didn't report door).
- East wall area (Cap/Basket).
I haven't looked at the East wall specifically from a good angle to see a door.
From TV (East), I see Cap and Basket.
Maybe the door is behind Cap?
Or in Room 1.
I started at (0,0). Saw Yellow Door (1, 3).
Room 1 is likely y < 3.
I didn't explore Room 1.
I should Query(yellow door) or similar if needed, but I have a good idea.

Wait, I have 12 steps left (max 19-7=12? No.
Start: 20.
1. Observe (-1) -> 19.
2. Jump, Obs (-1) -> 18. (Jump 0 cost?) No, Jump is a move. The rules don't specify move cost, but "Minimize total COST". Usually Move=1? No, "Minimize total COST while building...".
Wait, Instructions say:
"Observe and Query action have costs: Observe(): 1, Query(obj): 2"
Movement actions (JumpTo, Rotate) are not listed with costs.
Usually steps are limited (20).
Step count:
1. Observe (19 left)
2. Jump, Observe (18 left)
3. Jump, Rotate, Observe (17 left)
4. Jump, Rotate, Observe (16 left)
5. Jump, Rotate, Observe (15 left)
6. Jump, Rotate, Observe (14 left)
7. Jump, Rotate, Observe (13 left)
8. Rotate, Observe (12 left) -> This was the last one.
I have 12 steps left.

I need to decide where the brown door is.
Hypothesis: Room 1.
I should go back to `yellow door`. Rotate to face South/West/East in Room 1.
Action plan:
1. JumpTo(yellow door).
2. Rotate(180) (to face South into Room 1).
3. Observe().

Wait, I am at TV facing East.
JumpTo(yellow door).
Orient: East.
I need to look into Room 1. Room 1 is South of Yellow Door.
So I should face South.
Rotate(-90) (East to South).
Observe.

Refining Map Coordinates for JSON:
Agent: at `television` (-1, 5), facing `east`.
Objects:
- `yellow door`: (1, 3). Facing? "on front wall" (from Room 1). So implies South-facing (connecting N to S). Or North-facing (from Room 1 perspective). Let's say North.
- `television`: (-1, 5). Facing East (since I saw Cap "front" from it).
- `cap`: (3, 5). Facing West (saw TV "front" from it? No, from Plant (S), TV was Front, Cap was Front-Left. From TV (E), Cap is Front. So Cap is East of TV).
- `basket`: (2, 7). Facing South?
- `plant`: (-1, 9). Facing South?

I need to output the JSON.
Agent facing "east" (cardinal).
Map includes all observed.

Final check on coordinates:
Yellow Door (1, 3).
TV (-1, 5).
Cap (3, 5).
Basket (2, 7).
Plant (-1, 9).

From Yellow Door (1, 3) facing N:
TV (-1, 5): dx=-2, dy=2. Front-Left. OK.
Cap (3, 5): dx=2, dy=2. Front-Right. OK.
Basket (2, 7): dx=1, dy=4. Front-slight-right. OK.
Plant (-1, 9): dx=-2, dy=6. Front-slight-left. OK.

From Plant (-1, 9) facing E:
Basket (2, 7): dx=3, dy=-2. Front-Right. OK.

From Basket (2, 7) facing N:
Plant (-1, 9): dx=-3, dy=2. Front-Left. OK.

From Plant (-1, 9) facing S:
TV (-1, 5): dx=0, dy=-4. Front. OK.
Cap (3, 5): dx=4, dy=-4. Front-Left. OK.
Basket (2, 7): dx=3, dy=-2. Front-Left. OK.
Yellow Door (1, 3): dx=2, dy=-6. Front-slight-left. OK.

From TV (-1, 5) facing E:
Cap (3, 5): dx=4, dy=0. Front. OK.
Basket (2, 7): dx=3, dy=2. Front-Left. OK.

Coordinates look consistent.

FINAL ANSWER:
{
"agent": {"position": [-1, 5], "facing": "east"},
"yellow door": {"position": [1, 3], "facing": "north"},
"television": {"position": [-1, 5], "facing": "east"},
"cap": {"position": [3, 5], "facing": "west"},
"basket": {"position": [2, 7], "facing": "south"},
"plant": {"position": [-1, 9], "facing": "south"}
}

THINK:
I need to construct the cognitive map based on my observations.
Initial position: (0,0), facing North.
Observation 1 (from 0,0, N): `yellow door` at front-slight-right, mid distance, on front wall.
Let's estimate coordinates. "Front wall" implies a wall at some Y. "Mid distance" is (2, 4]. Le...

{
  "agent": {
    "position": [
      -1,
      5
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "television": {
    "position": [
      -1,
      5
    ],
    "facing": "east"
  },
  "cap": {
    "position": [
      3,
      5
    ],
    "facing": "west"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "south"
  },
  "plant": {
    "position": [
      -1,
      9
    ],
    "facing": "south"
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      5
    ],
    "facing": "east"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      0,
      5
    ],
    "facing": "east"
  }
}

THINK:
I am currently at the `television`. I just rotated 180 degrees from West, so I am now facing East.
My observation is:
- `cap`: front, near, facing forward.
- `basket`: front-left, mid distance.

Relative to me (facing East = local +y):
- "front" means roughly along the +y axis.
- "near" usually implies distance bin (0, 2]. Let's say y=2.
- `cap` position: [0, 2] approximately.
- `cap` facing: "forward". If the object faces forward relative to my view, and I am looking at its front? Or does "facing forward" mean it faces the same direction as me? The prompt says "facing forward" in the observation. Standard interpretation: The object's orientation is such that it "faces" the agent? Or faces the direction "forward"?
- In previous turns: "facing forward" meant facing the agent (opposite to agent's facing).
- Let's assume "facing forward" means it is facing me (South? No, I am facing East. So it faces West?).
- Or "facing forward" means its intrinsic 'front' is aligned with my 'front' (East)?
- Let's look at the "North" assumption provided: "Assume your current facing direction is called 'north': cap is east...". This is confusing. The prompt says "Assume your current facing direction is called 'north'".
- Let's stick to the relative coordinates.
- `cap` is "front" -> +y. Distance "near" -> 2. Position: [0, 2].
- `cap` facing: "facing forward". If I am facing East (+y locally), and it faces forward, maybe it faces +y? Or faces me (-y)? "Facing forward" usually implies facing the viewer in these text games, or facing the same way? Let's check the first observation: "television: front-left... facing forward".
- Let's just use "facing": "+y" or "-y". If "facing forward" means facing the agent, it's -y. If it means facing the same direction, it's +y. Given "facing right" was used for cap before (when viewed from North), and now viewed from West (looking East) it's "facing forward".
- From North (Yellow Door): Cap was front-right (East), facing Right (East).
- Now I am West of it, looking East. If it faces East, and I look East, I see its back? Or if "facing right" meant facing West?
- Let's rely on the observation text "facing forward". I will map it to "-y" (facing me) or "+y" (facing away). Usually "facing you" is explicit. "Facing forward" might mean its front is towards +y (East). Let's guess "+y".
- Actually, let's look at previous data. From Door (North): Cap facing Right (East). I am now facing East. So Cap is facing same direction as me. So "+y".

- `basket`: front-left, mid distance.
- Front-left -> x < 0, y > 0.
- Mid distance -> (2, 4]. Let's say dist 4.
- Angle approx 45 deg left? x = -2, y = 3? Or x=-1, y=3?
- Let's approximate: [-2, 3].

Wait, the prompt asks for "facing" using +x/-x/+y/-y.
I need to map the "facing forward" string to this.
If "facing forward" = same direction as agent = +y.
The `basket` has no facing info in the observation.

JSON structure:
{
"origin": "agent",
"objects": {
"cap": {"position": [0, 2], "facing": "+y"},
"basket": {"position": [-2, 3]}
}
}

Let's refine coordinates.
"near" (0, 2]. Let's use 2.
"mid distance" (2, 4]. Let's use 4.
`cap`: front (0 degrees). y=2, x=0.
`basket`: front-left (approx -45 to -22.5). Distance 4.
x = 4 * sin(-30) = -2. y = 4 * cos(-30) = 3.5. Integer approx: [-2, 3] or [-2, 4].

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"cap": {"position": [0, 2], "facing": "+y"},
"basket": {"position": [-2, 3]}
}
}

THINK:
I am currently at the `television`. I just rotated 180 degrees from West, so I am now facing East.
My observation is:
- `cap`: front, near, facing forward.
- `basket`: front-left, mid distance.

Relative to me (facing East = local +y):
- "front" means roughly along the +y axis.
- "near" usual...

{
  "origin": "agent",
  "objects": {
    "cap": {
      "position": [
        0,
        2
      ],
      "facing": "+y"
    },
    "basket": {
      "position": [
        -2,
        3
      ]
    }
  }
}

{
  "cap": {
    "position": [
      0,
      2
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      -2,
      2
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "cap": {
      "position": [
        0,
        2
      ],
      "facing": "+y"
    },
    "basket": {
      "position": [
        -2,
        3
      ]
    }
  }
}

THINK:
I need to identify which candidate points (A-F) are in unexplored regions based on my exploration so far.

My exploration path:
1. **Start (Room 1, (0,0), facing North):** Observed `yellow door` (front-slight-right). Room 1 seems to be the bottom room.
2. **Jump to `yellow door` (facing North):** Saw into Room 2. Objects: `television` (West), `cap` (East), `basket` (NE), `plant` (NW).
3. **Jump to `plant` (NW Room 2), Rotate 90 (Face East):** Saw `basket`.
4. **Jump to `basket` (NE Room 2), Rotate -90 (Face North):** Saw `plant`.
5. **Jump to `plant` (NW Room 2), Rotate 180 (Face South):** Saw `television`, `cap`, `basket`, `yellow door`.
6. **Jump to `television` (W Room 2), Rotate 90 (Face West):** Saw nothing.
7. **Rotate 180 (Face East):** Saw `cap`, `basket`.

My current location is at the `television` in Room 2, facing East.
Room 2 is the upper room in the map (above the first '+').
The `yellow door` connects Room 1 (bottom) and Room 2 (top). The map shows a door connecting a bottom room and a top room.
The coordinates (0,0) are bottom-left. The map matches: Room 1 is roughly (1,1) to (6,6). Room 2 is roughly (3,7) to (9,13).

Let's evaluate the candidates:
- **A:** Located in the bottom room (Room 1), on the left side. I started at (0,0) facing North and saw the yellow door. I did *not* look West or explore the left side of Room 1. So A is likely unexplored.
- **B:** Located in Room 1, near the top right corner. From (0,0) facing North, this area might have been on the periphery or occluded? But wait, the yellow door was "front-slight-right". B is to the right of the door area. I haven't explicitly looked at that corner.
- **C:** Located in Room 1, top right corner. Same as B.
- **D:** Located in Room 1, bottom right. I haven't looked there.
- **E:** Located in Room 1, center-ish right.
- **F:** Located in Room 1, center-ish right.

Wait, looking at the map provided in the probe:
Room 2 is the top room (where I am). The `*` is at `television`.
The candidates A, B, C, D, E, F are all in the *bottom* room (Room 1).
Wait, let's look closer at the ASCII map.
The `+` connects the top block and bottom block.
Top block has `*`.
Bottom block has candidates.
The bottom block has another `+` (door) at the bottom? No, `#......+......#` is a wall with a door?
Actually, the map shows:
Top Room (Room 2): `###..*...######`
Connection: `######+########` (Yellow Door?)
Bottom Room (Room 1): Has `A`, `B`, `C`, `D`, `E`, `F`.
Also has a door `+` on the *right* wall? ` #......+......#` is a horizontal line? No, it looks like a south wall of a room or a partition?
Let's trace the walls.
`######+########` is the wall between the two main spaces.
The bottom space is bounded by `#` on left, `#` on right.
Inside the bottom space, there are candidates.
And there is a `+` in the middle of the bottom area? ` #......+......#`. Is that a door or a wall?
It looks like a horizontal wall segment with a door. Or maybe it's the bottom wall of Room 1?
Wait, the `+` is at `(x, y)` position.
Let's assume the candidates are in Room 1.
I started in Room 1 and immediately jumped to the yellow door. I only observed North. I saw the yellow door.
I did *not* scan Room 1. I haven't seen the West side (A), the East side (B, C, E, F, D).
Therefore, *all* points in Room 1 are largely unexplored/unobserved, except maybe the direct path from start to yellow door.
Point A is West of start. Unobserved.
Points B, C, E, F are East of start. Unobserved.
Point D is South-East. Unobserved.

So, all candidates A, B, C, D, E, F seem to be in unexplored regions of Room 1.
However, I need to be precise.
Start pos: (0,0) facing North.
Observe(): Saw yellow door (front-slight-right).
FOV is 90 degrees (North-West to North-East).
Points directly North were observed.
Points East or West were not.
A is West. Unexplored.
B, C are North-East? If "front-slight-right", maybe observed?
Yellow door was `mid distance` (2-4m).
If B, C are `near` the door, I might have seen them. But I didn't report objects there.
Candidates usually represent "fog". If I haven't looked there, it's unexplored.
I have only looked North from (0,0).
My cone covered the central corridor to the door.
A is to the left.
B, C, E, F are to the right.
D is to the right-down?
Given I moved quickly to Room 2, Room 1 is mostly unknown.

Let's check the map layout again.
`#....BC#......#`
`#....EF#......#`
`#.A....#......#`
`#......+......#`
`#.....D#......#`

The `+` in the middle of the bottom block suggests a wall separating two rooms or a door to outside?
Or maybe Room 1 is the area with A. And there is a Room 3 connected via the second `+`.
If there is a door at the bottom `+` or right `+`, that leads to Room 3.
I haven't found the brown door.
The candidates are in the bottom area.
I have not explored the bottom area properly.
So A, B, C, D, E, F are all likely candidates.
However, usually, "unexplored" means "not yet seen".
I saw the path from (0,0) to the yellow door.
A is clearly off-path.
B, C, E, F are on the right side.
D is below the second `+`? Wait.
Line ` #......+......# `
Is that a wall? If so, D is in another room (Room 3?).
Or is it the Start Room?
If Start was (0,0), and I faced North.
If (0,0) is bottom-left.
Then A is at approx (2, 4).
Start was (0,0)? The map has (0,0) at bottom-left.
If I started at (0,0) and saw yellow door at mid distance (approx 3-4 units), and yellow door is at `######+########`.
The map shows the top door is at y=7 or 8.
(0,0) to (x, 7) is distance 7. That's "slightly far" or "far".
Wait, distance bins: near (0-2), mid (2-4), slightly far (4-8).
So yellow door at mid/slightly far matches.
The bottom `+` is at y=4 or 5?
If there is a door at y=5, I would have seen it?
Or maybe I started North of it?
"You current (initial) position is in room 1... treat your initial position as the origin (0, 0)".
If (0,0) is in Room 1.
The map shows candidates.
It's safest to assume all points in the room I left immediately are unexplored, especially the corners.
A is West.
B, C, D, E, F are East/South.
I will mark all of them as unexplored.

Refining:
A is definitely unexplored (West).
B, C, E, F are East. I looked North. My FOV (North-West to North-East) might have clipped the area, but I didn't see objects.
D is "behind" the `+` wall? Or just South-East?
I'll select all.

Wait, let's look at the "Fog Probe" instructions. "Select the points that are located in unexplored/unobserved regions."
I've only been in Room 2 (Top) and the doorway.
Room 1 (Bottom) has A, B, C, D, E, F.
I only looked North from (0,0).
A is West -> Unobserved.
E, F are East -> Unobserved (outside 90 deg cone? 45 deg right is limit).
B, C are North-East -> Might be in FOV?
But if I haven't confirmed them as free space or objects, they are candidates for exploration.
Also, the brown door is missing. It's likely in Room 1.
I'll flag all A-F as unexplored.

Re-evaluating B/C.
If I am at (0,0) facing North.
(0,0) to B/C (approx (5, 6)?). Angle is approx 45-60 deg.
FOV is +/- 45 deg.
So B/C are likely *outside* the FOV or on the edge.
So they are unobserved.

D is definitely unobserved (behind/side).

So, A, B, C, D, E, F.

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

THINK:
I need to identify which candidate points (A-F) are in unexplored regions based on my exploration so far.

My exploration path:
1. **Start (Room 1, (0,0), facing North):** Observed `yellow door` (front-slight-right). Room 1 seems to be the bottom room.
2. **Jump to `yellow door` (facing Nor...

###############
###......######
###......######
###......######
###......######
###..*...######
###......######
######+########
#......########
#....BC#......#
#....EF#......#
#.A....#......#
#......+......#
#.....D#......#
########......#
###############

You rotated clockwise 180°. You observe:
• cap: front, near, facing forward
• basket: front-left, mid distance
Assume your current facing direction is called "north":
• cap is east, near to basket.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 180°. You observe:
• cap: front, near, facing forward
• basket: front-left, mid distance
Assume your current facing direction is called "north":
• cap is east, near to basket.
You have a maximum of 12 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts o...

I am at `television`, facing East.
I see `cap` (front) and `basket` (front-left).
I do not see the `brown door`.
This suggests the brown door is not immediately visible on the East wall from this angle, or it's obscured, or it's not there.
However, I am looking across the room.
Let's go to `cap` and inspect the East wall closely.
`Cap` is "front".
Action: JumpTo(cap).
Orientation at `cap`: East.
I will check the East wall.
Then I can also check the South wall (near yellow door) again from a better angle, or check Room 1.
If I don't see the brown door at the East wall, I will assume it's in Room 1.

Action: JumpTo(cap), Observe().
(I am already facing East, so looking at the wall).

I am at `television`, facing East.
I see `cap` (front) and `basket` (front-left).
I do not see the `brown door`.
This suggests the brown door is not immediately visible on the East wall from this angle, or it's obscured, or it's not there.
However, I am looking across the room.
Let's go to `cap` and...

THINK:
I need to construct the JSON map based on my observations.
Initial state: Agent at (0,0) facing North in Room 1.
1. Observe at (0,0) facing North:
- `yellow door`: front-slight-right, mid distance, on front wall.
- Let's estimate coordinates. "Mid distance" is (2,4]. Let's say 3 or 4 units away.
- Angle "front-slight-right" is (0, 22.5]. Let's say roughly (1, 4) or (2, 4).
- "On front wall" suggests y is positive.
- Agent jumped to `yellow door`. Position becomes the door's position.
- Let's fix `yellow door` at approx (1, 4) for now.

2. At `yellow door` facing North (into Room 2):
- `television`: front-left, mid distance (facing forward). Relative to door (facing N): West-ish.
- `cap`: front-right, mid distance (facing right). Relative to door (facing N): East-ish.
- `basket`: front-slight-right, slightly far. Relative to door (facing N): North-East.
- `plant`: front-slight-left, slightly far. Relative to door (facing N): North-West.
- Constraints:
- `television` is west, near to `cap`. (Wait, "television is west, near to cap" from the prompt seems to be a relative description provided by the system, likely meaning in the global frame or room frame. If door faces North, Left is West, Right is East. TV West, Cap East makes sense).
- `cap` is south, near to `basket`. (Wait, Cap is mid distance, Basket is slightly far. So Basket is North of Cap. Cap is South of Basket. Correct).

- Let's assign rough coordinates relative to `yellow door` at (1, 4):
- `television`: (-2, 6) ? (Mid distance ~3. Left ~West). Let's say x < 1, y > 4.
- `cap`: (4, 6) ? (Mid distance ~3. Right ~East). Let's say x > 1, y > 4.
- `basket`: (3, 9) ? (Slightly far >4. Right-ish).
- `plant`: (-1, 9) ? (Slightly far >4. Left-ish).

3. Jump to `plant`. Rotate 90 (Clockwise).
- `plant` is approx (-1, 9). Facing North originally? No, "JumpTo ... Orientation does NOT change".
- At `yellow door` I was facing North. Jump to `plant`. Agent at `plant`, facing North.
- Rotate 90 -> Agent facing East.
- Observe: `basket`: front-right, mid distance.
- From `plant` (facing East), Front is East, Right is South. "Front-right" is South-East.
- Previous estimate: Plant (-1, 9), Basket (3, 9).
- Vector Plant->Basket is (4, 0) i.e. East.
- If I face East, Basket should be "Front".
- Observation says "front-right". This implies Basket is South of the East-vector.
- Maybe Plant is at (-1, 10) and Basket is at (3, 8)?
- Let's refine.

4. Jump to `basket`. Rotate -90 (Counter-Clockwise).
- Agent at `basket`. Facing East -> Rotate -90 -> Facing North.
- Observe: `plant`: front-left, mid distance.
- From `basket` (facing North), Front is North, Left is West. "Front-left" is North-West.
- This contradicts the previous relative position if Basket was South-East of Plant.
- If Basket is SE of Plant, then Plant is NW of Basket.
- From Basket facing North, NW is "front-left". This matches.
- So Plant is NW of Basket.
- Basket is SE of Plant.
- Let's adjust coordinates:
- Plant: (0, 10)
- Basket: (3, 8)
- Plant is NW of Basket (dx = -3, dy = +2).
- Distance sqrt(9+4) ~ 3.6 (mid distance). Matches.

5. Jump to `television`. (Failed).
- `television` not visible from `basket` (facing North).
- TV is likely South-West. From Basket (N), SW is "rear-left" (beyond FOV). Consistent.

6. Jump to `plant`. Rotate 180.
- Agent at `plant` (0, 10). Facing North -> Rotate 180 -> Facing South.
- Observe:
- `television`: front, mid distance. (Front = South). So TV is South of Plant.
- `cap`: front-left, slightly far. (Front-Left = South-East). Cap is SE of Plant.
- `basket`: front-left, mid distance. (Front-Left = South-East). Basket is SE of Plant.
- `yellow door`: front-slight-left, slightly far. (Front-Left = South-East). Door is SE of Plant.
- Refined coordinates:
- Plant: (0, 10).
- TV: South of Plant. Let's say (0, 7) or (-1, 6)? "Mid distance". Let's say (0, 6).
- Basket: SE of Plant. (3, 8) fits "mid distance" (~3.6) and SE direction.
- Cap: SE of Plant. "Slightly far" (>4). If Cap is near Basket but South of it?
- Yellow Door: SE of Plant. "Slightly far". Door was at (1, 4). Distance from (0, 10) to (1, 4) is sqrt(1+36) ~ 6. Fits "slightly far".

7. Jump to `television`. Rotate 90.
- Agent at `television` (0, 6). Facing South -> Rotate 90 -> Facing West.
- Observe: Nothing. West wall is empty.

8. Rotate 180.
- Agent at `television` (0, 6). Facing West -> Rotate 180 -> Facing East.
- Observe:
- `cap`: front, near. (Front = East). Cap is East of TV.
- `basket`: front-left, mid distance. (Front-Left = North-East). Basket is NE of TV.
- Refined coordinates:
- TV: (0, 6).
- Cap: East of TV. "Near" (<=2). Let's say (2, 6) or (3, 6)?
- Earlier: Cap was SE of Plant (0, 10). (2, 6) is SE. Distance sqrt(4+16) ~ 4.5.
- Earlier: Cap was Front-Right from Door (1, 4) facing N. (2, 6) is NE of (1, 4). Matches.
- Relation: "Cap is South, near to Basket". Basket (3, 8). Cap (3, 6) is South of Basket. Distance 2 ("near").
- Relation: "TV is East, near to Cap". (Wait, prompt said "television is west, near to cap").
- If TV is (0, 6) and Cap is (2, 6). TV is West of Cap. Matches.
- Distance 2. Fits "near".

9. Jump to `cap`. Observe.
- Agent at `cap` (2, 6) or (3, 6). Facing East.
- Observe: Nothing. East wall is empty.

Summary of positions:
- `yellow door`: (1, 4)
- `television`: (0, 6), Facing: forward? From door it was "facing forward". Door faces N. So TV faces South?
- Observation 2: "television... facing forward". Agent facing North. If object faces "forward", it faces South (towards agent)? Or faces the same direction? Usually "facing forward" means facing the agent. So TV faces South.
- Let's check Observation 6 (from Plant facing South): "television... facing backward". Agent faces South. Backward is North. So TV faces North?
- Wait. "facing forward" usually means the object's front is towards the viewer.
- Obs 2 (Agent facing N): TV faces "forward" -> TV faces South.
- Obs 6 (Agent facing S): TV faces "backward" -> TV faces South (Agent's back is North). If "facing backward" means facing the direction of agent's back?
- Let's ignore facing for objects unless specified clearly. The prompt asks for facing in JSON if object has facing direction.
- Obs 2: "facing forward". Obs 6: "facing backward".
- Let's assume TV faces East or something?
- Actually, from Obs 2 (Agent N): "television... facing forward". Usually means its front is facing South.
- From Obs 6 (Agent S): "television... facing backward". Agent's backward is North. So TV faces North.
- Contradiction? Or "facing backward" means facing away from agent?
- Let's stick to coordinates.

- `cap`: (3, 6). Facing: Obs 2 (Agent N) "facing right" -> East. Obs 6 (Agent S) "facing left" -> East. Consistent. Cap faces East.
- `basket`: (3, 8). No facing info.
- `plant`: (0, 10). No facing info.
- `yellow door`: (1, 4). On front wall relative to start? Start (0,0). Door is at (1,4).
- `agent`: Currently at `cap` (3, 6). Facing East.

Wait, I need to place the agent correctly.
Last action: `JumpTo(cap)`. Agent is at `cap`.
Orientation: Last rotation was to East (at TV). Jump doesn't change orientation. So Agent faces East.

JSON Map:
Agent: pos ~[3, 6], facing "east".
Yellow door: pos ~[1, 4].
Television: pos ~[0, 6]. Facing "south" (based on Obs 2 "facing forward" to North-facing agent).
Cap: pos ~[3, 6]. Facing "east".
Basket: pos ~[3, 8].
Plant: pos ~[0, 10].

Let's adjust to integer coordinates that fit bins nicely.
Door (1, 4).
TV (0, 6). Dist to Door: sqrt(1+4)=2.2 (mid). OK.
Cap (3, 6). Dist to Door: sqrt(4+4)=2.8 (mid). OK.
Basket (3, 8). Dist to Cap: 2 (near). OK.
Plant (0, 10). Dist to Basket: sqrt(9+4)=3.6 (mid). OK.
Plant Dist to Door: sqrt(1+36)=6 (slightly far). OK.
TV Dist to Cap: 3 (near-ish, bin is (2,4] mid). Prompt said "near" (<=2)?
- "television is west, near to cap". Dist 3 is mid distance.
- Maybe scale down x?
- Door (1, 4).
- TV (0.5, 6)? No integers.
- Maybe Door (2, 4). TV (0, 6). Dist sqrt(4+4)=2.8.
- Cap (4, 6). Dist sqrt(4+4)=2.8.
- Dist TV-Cap = 4 (mid). Not near.
- Prompt said "near".
- Maybe they are closer.
- Door (2, 4).
- TV (1, 6). Cap (3, 6). Dist = 2 (near).
- Basket (3, 8). Dist to Cap = 2 (near).
- Plant (1, 8)?
- Plant to Basket: Dist 2 (near).
- Obs: Plant-Basket was mid distance (~3).
- Plant (0, 9), Basket (3, 8)? Dist sqrt(9+1) = 3.16. OK.
- Plant (0, 9) to Door (2, 4): sqrt(4+25) = 5.3 (slightly far). OK.
- Basket (3, 8) to Door (2, 4): sqrt(1+16) = 4.1 (slightly far). OK.
- TV (1, 6) to Door (2, 4): sqrt(1+4) = 2.2 (mid). OK.
- Cap (3, 6) to Door (2, 4): sqrt(1+4) = 2.2 (mid). OK.
- TV (1, 6) to Cap (3, 6): Dist 2 (near). OK.
- Cap (3, 6) to Basket (3, 8): Dist 2 (near). OK.

Coordinates:
Yellow door: [2, 4]
TV: [1, 6], facing "south".
Cap: [3, 6], facing "east".
Basket: [3, 8].
Plant: [0, 9].

Agent at `cap` [3, 6], facing "east".

One issue: I haven't found the Brown Door.
I am in the middle of exploration. I need to output the CURRENT map.
I will output the objects I have observed.

FINAL ANSWER:
```json
{
"grid": "N x M",
"agent": {"position": [3, 6], "facing": "east"},
"yellow door": {"position": [2, 4]},
"television": {"position": [1, 6], "facing": "south"},
"cap": {"position": [3, 6], "facing": "east"},
"basket": {"position": [3, 8]},
"plant": {"position": [0, 9]}
}
```

THINK:
I need to construct the JSON map based on my observations.
Initial state: Agent at (0,0) facing North in Room 1.
1. Observe at (0,0) facing North:
- `yellow door`: front-slight-right, mid distance, on front wall.
- Let's estimate coordinates. "Mid distance" is (2,4]. Let's say 3 or 4 un...

{
  "grid": "N x M",
  "agent": {
    "position": [
      3,
      6
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      2,
      4
    ]
  },
  "television": {
    "position": [
      1,
      6
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      3,
      6
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      3,
      8
    ]
  },
  "plant": {
    "position": [
      0,
      9
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  }
}

THINK:
I am at the `cap`. I jumped from `television` (where I was facing East). So my orientation is East.
I observed "No objects in field of view".
This means looking East from `cap` reveals nothing (just wall).
So the Local Cognitive Map should be empty of objects.
However, the prompt asks to represent the scene as a JSON map. If no objects are observed, the "objects" dictionary should be empty.

Wait, I just observed "No objects in field of view".
This means my current view contains nothing.
So the JSON should reflect that.

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

THINK:
I am at the `cap`. I jumped from `television` (where I was facing East). So my orientation is East.
I observed "No objects in field of view".
This means looking East from `cap` reveals nothing (just wall).
So the Local Cognitive Map should be empty of objects.
However, the prompt asks to repr...

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

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

THINK:
My current position is at the `cap` in Room 2 (the upper room). I am facing East. I observed "No objects in field of view".
The map shows Room 2 (upper) and Room 1 (lower).
The yellow door connects them.
I am at `*` (cap) in Room 2.
My previous observations in Room 2 covered:
- From yellow door looking North: Saw TV (West), Cap (East), Basket (NE), Plant (NW).
- From Plant looking East: Saw Basket.
- From Basket looking North: Saw Plant.
- From Television looking West: Wall.
- From Television looking East: Saw Cap, Basket.
- From Cap looking East (current): Wall (seen nothing).

I have pretty much explored Room 2. The walls seem to be solid. I haven't seen a brown door.
The candidates A-F are in Room 1 (the lower room).
I started in Room 1 at (0,0) (presumably near bottom-center or left? The map shows `+` at (7,4) roughly? No, the map coords: (0,0) bottom-left. The door is at (6, 8)? No, let's count.
Map size seems 15 wide.
Room 1 is the bottom left/center area.
Room 2 is the top left/center area.
Room 3 is likely the unvisited area (maybe the right side?).
The candidates A, B, C, D, E, F are in Room 1.
I only stood at the start (near D/A?) and looked North. I saw the yellow door.
I haven't looked West, East or South in Room 1.
Areas A, B, C, D, E, F are all in Room 1. A is West, B is East, C is near door, D is center, E/F center.
Since I haven't looked around in Room 1 except North, the side and back areas are unexplored.
Especially "A" (West wall area), "B" (East wall area), "D" (South/Start area - I stood there but maybe didn't see behind me).
Wait, I stood at start and looked North. My FOV is 90 deg.
I saw the yellow door at mid distance.
I did not see the rest of the room.
The Fog Probe asks for "unexplored/unobserved regions".
Since I haven't scanned Room 1 properly, all points in Room 1 that are not in the direct line of sight to the door are candidates.
However, I have seen the path to the door.
Point C is near the door. Likely observed.
Points E, F are in the middle. Likely observed or close.
Points A, B, D are further out.
Actually, I just need to identify which points are in unexplored regions.
I have validly explored Room 2.
Room 1 is mostly unexplored.
Also, there is a third room to the right (East of Room 1 and Room 2) which I haven't accessed. It looks like the area with no points? Or maybe B is near the boundary?
Wait, the map shows:
Room 1 (bottom left).
Room 2 (top left).
Another room to the right (East) connected by a door?
Look at the map:
Row 8 has a `+` connecting Room 1 and Room 2.
Row 4 (approx) has a `+` connecting Room 1 and the Room to the right?
Let's check the map structure.
`#######......#` on the right side.
`#.A....+......#`
There is a door `+` on the right wall of Room 1!
So Room 3 is to the East of Room 1.
I missed this door because I didn't look East in Room 1.
The points A, D, E, F, C, B are in Room 1.
A is West.
D is South-West.
E, F are central.
C is North (near yellow door).
B is East (near the potential brown door?).
The unexplored regions are definitely the sides and back of Room 1, and the entire Room 3.
The question asks to select points located in unexplored/unobserved regions.
A: Unobserved (West side).
B: Unobserved (East side/near brown door).
C: Observed? I saw the door, C is near it. Probably observed.
D: Unobserved (Behind me/start).
E, F: Observed? In the cone.
So A, B, D are the strongest candidates. E, F maybe. C unlikely.
Let's look closer.
Agent started at (0,0) facing North. Cone is 45 deg left/right.
If start is (something, something), let's assume centered relative to door.
Door is at top of Room 1.
If I saw door, I saw the middle corridor.
A is to the left (West). Unobserved.
B is to the right (East). Unobserved.
D is behind/at start. If I started there, I observed it? No, `Observe` sees "from current position". If I stand on D and look North, D is not "observed" in the sense of "what's at D", but I am at D. However, usually "unexplored" means "haven't seen what's there". I know empty space is there.
But B is near a door I missed. A is a corner I missed.
The prompt asks for points in "unexplored/unobserved regions".
A and B are definitely in the unobserved side cones.
D is where I started? Or behind?
Let's assume A, B, D. Maybe E/F are central enough.
Actually, look at the door to the right. It's at the same level as A?
The `+` is on the vertical wall separating left and right rooms.
So B is near that door.
A is on the opposite side.
I will select A, B, D as they are in the blind spots of my initial single observation.
Also, looking at the map, there is a door `+` at the East wall of Room 1.
The brown door is likely there.
So B is very important.
A is also unobserved.
D is the start area (if I moved immediately, I might not have seen "behind" me, but I started there).
I'll stick with A, B, D. E and F are likely in the view cone to the yellow door. C is definitely in the view cone.

Refined check:
Map:
`#..EF.B#......#`
`#.A....+......#`
`+` is on the wall between the room with A/B/etc and the empty space on right.
Wait, `+` is at `#.A....+......#`. So `+` is on the wall.
So B is close to the door.
A is far left.
D is far left down.
Start position (0,0) - likely near D?
If I faced North and saw the yellow door (top), A (West) and B (East) were likely outside the 90 deg FOV if the room is wide.
Start pos: typically (0,0). If room is 5 wide, and I am at 2, facing North.
The door is at x=something.
If I saw the door, I saw the center.
Sides A and B are unobserved.
So I select A, B. D is also likely unobserved if it's in the corner or behind.
Let's select A, B, D.

Wait, is `C` unobserved? It's right in front of the yellow door. I saw the door, so I saw the space in front. C is observed.
E, F are between start and door. Observed.
So A, B, D.

Actually, looking at the ASCII map provided in the probe:
Room 1 is the bottom-left rectangle.
Room 2 is the top-left rectangle.
Room 3 is the right rectangle (implied by `......`).
There is a `+` between Room 1 and Room 3.
This confirms the brown door is in Room 1, East wall.
I missed it because I only looked North.
The points in unexplored regions of Room 1 are A (West) and B (East/Door area) and D (South West).
Also, strictly speaking, Room 3 is completely unexplored, but there are no points labeled there?
Wait, the dots `......` are floor.
There are no letters in Room 3?
Ah, look closely.
`#..EF.B#......#` -> B is inside Room 1.
`#.A....+......#` -> A is inside Room 1. `+` is the door.
The letters are all in Room 1.
So the answer should be the subset of {A, B, C, D, E, F} that is unobserved.
A: West side. Unobserved.
B: East side. Unobserved.
D: South-West. Unobserved.
E, F: Center. Likely Observed.
C: North Center. Observed.

So {A, B, D}.

Wait, is D unobserved? If I started at (0,0) and D is at (2,2) and I faced North...
Actually, I don't know the exact coordinates.
But generally, side and back areas are unobserved.
I will select A, B, D.

Actually, let's look at the density. A, D are on the left. B is on the right.
E, F are in the middle.
If my FOV is 90 deg (cone), and I am at bottom center facing up:
I see a triangle.
A (Left) and B (Right) are outside.
D (Bottom Left) is outside.
So A, B, D.

Double check C. C is near the top door. I saw the door. So I saw C.
Double check E, F. They are in the middle path. Likely seen.
So A, B, D.

Wait, looking at the map again:
`#..EF.B#`
`#.A....+`
`#......#`
`#..D...#`
D is in the middle of the room, vertically?
If I started at the bottom `########......#` (bottom wall).
D is in the lower part.
E, F are in the upper part.
A is left. B is right.
If I start at bottom center and look North:
I see a cone.
D is likely inside the cone if it's in front of me.
If D is at the side, maybe not.
But A and B are definitely at the sides.
Is D "unobserved"?
The prompt says "Minimize total COST while building a complete and accurate map".
Fog probe: "Select the points that are located in unexplored/unobserved regions."
I'll assume D is observed if it's central-ish.
But A and B are definitely unobserved.
Let's check B. B is near the wall with the door `+`.
I definitely didn't see that door.
So B is unobserved.
A is opposite. Unobserved.
What about D?
If D is (x, y) and I am (x_start, y_start).
If D is near the wall, and I am central, maybe D is observed?
But D is labeled `D`.
Let's look at the relative positions.
`A` is row 4 from bottom.
`D` is row 2 from bottom? No.
Map:
Rows from bottom up (approx):
Row 1: # (Wall)
Row 2: floor, D is here. `..D...`
Row 3: floor, A is here `A`.
Row 4: floor, E, F, B are here.
Row 5: floor, C is here.
Row 6: Wall/Door.

If I started at Row 2 (where D is) or Row 1 (Wall)?
Usually start is just inside.
If I started near D and looked North.
I would see E, F, C, Door.
I would NOT see A (Left), B (Right).
D is at my position or behind/side?
If D is at my position, it is "observed" (I know it's empty).
If D is to my side, I might not see it.
However, usually the agent knows where it has been.
If I started at D, D is explored.
If I started at (0,0) and D is (2,2)...
Let's assume the start is central bottom.
I'll go with A and B as the clear unobserved regions. D is ambiguous but likely close to start/observed.
Actually, let's include D to be safe?
No, if D is close to the trajectory, it's observed.
A and B are lateral.
So ["A", "B"].

Let's re-read "You observe: yellow door: front-slight-right".
My start pose: facing North.
Door is front-slight-right.
This means I am to the LEFT of the door.
Or the door is to the RIGHT of the center.
If I am to the left, my right side FOV might cover more of the right side?
"front-slight-right" is (0, 22.5].
So the door is slightly to the right.
This means I am somewhat aligned with it but it's to the right.
If I am left-aligned, my left FOV is limited (walls). My right FOV covers the center-right.
So maybe I saw B?
But I didn't see the brown door (which is at `+` near B).
So B is unobserved.
What about A? A is on the Left.
If I am on the Left side (relative to room), and look North.
My Left FOV hits the West wall quickly.
A is near the West wall.
I probably saw the wall near A.
But "unexplored region" usually implies significant missing info.
The brown door is the key missing info. It's at B.
A is just a corner.
However, the Fog Probe asks for "unexplored/unobserved".
I'll select A and B.

Final check on D.
D is "behind" A? No, D is below A.
If I moved North, I moved away from D.
Did I see D? Only if I looked down/back. I didn't.
So D is unobserved (unless I started exactly on it).
But the prompt says "start position is origin".
If D is origin, it's observed.
If D is not origin, and I looked North, I missed D.
I will assume D is unobserved.
So A, B, D.

Wait, is C unobserved?
C is near the door. I saw the door.
So C is observed.

E, F?
They are in the middle.
Probably observed.

So A, B, D.

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

THINK:
My current position is at the `cap` in Room 2 (the upper room). I am facing East. I observed "No objects in field of view".
The map shows Room 2 (upper) and Room 1 (lower).
The yellow door connects them.
I am at `*` (cap) in Room 2.
My previous observations in Room 2 covered:
- From yellow do...

###############
###......######
###......######
###......######
###......######
###....*.######
###......######
######+########
#....C.########
#..EF.B#......#
#......#......#
#..D...#......#
#.A....+......#
#......#......#
########......#
###############

You jumped to cap. 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 jumped to cap. 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 am at `cap`, facing East. No objects visible.
This means the East wall of Room 2 is also empty of doors/objects.
So, `brown door` is NOT in Room 2 (North, West, East walls checked). It's unlikely on the South wall because I saw the yellow door there and the wall seemed empty otherwise (from Plant facing South).

Conclusion: The `brown door` is in Room 1.
I need to return to Room 1.
I am at `cap`. I need to go to `yellow door`.
`Yellow door` is not in my current FOV (facing East).
I need to find `yellow door`.
From `television` (facing South, before West rotation), I saw `yellow door` to the left.
From `cap`, `yellow door` should be nearby (South).
Let's Rotate(90) (face South) or Rotate(-90) (face North) to find something.
Actually, `yellow door` is South of Room 2. `Cap` is near `yellow door`.
If I Rotate(90) (face South), I should see `yellow door`.
Then JumpTo(`yellow door`).

Sequence:
1. Rotate(90). Observe() to confirm door.
2. JumpTo(yellow door).

Wait, I can combine. But I can't Jump to something not in FOV.
So:
Step 1: Rotate(90), Observe().

I am at `cap`, facing East. No objects visible.
This means the East wall of Room 2 is also empty of doors/objects.
So, `brown door` is NOT in Room 2 (North, West, East walls checked). It's unlikely on the South wall because I saw the yellow door there and the wall seemed empty otherwise (from Plant ...

THINK:
I need to construct a cognitive map of the environment based on my observations so far.

**Coordinate System:**
* Origin (0, 0) is my initial position in Room 1.
* North is +y, East is +x.

**Room 1:**
* **Initial Position:** (0, 0).
* **Yellow Door:**Observed from (0,0) facing North as "front-slight-right, mid distance".
* "Mid distance" is (2, 4]. Let's estimate 3 or 4 units away.
* "Front-slight-right" (0 to 22.5 degrees).
* Let's place the yellow door roughly at (1, 3) or (1, 4). Let's assume (1, 3).
* It is on the "front wall" (North wall of Room 1 / South wall of Room 2).

**Room 2:**
* **Yellow Door (from Room 2 side):** When I jumped to it, I was at (1, 3).
* **Television:**
* From Yellow Door (facing North): "front-left, mid distance". Mid distance ~3 units. Front-left is NW. Estimated pos: (1-2, 3+2) = (-1, 5).
* From Plant (facing South): "front".
* **Cap:**
* From Yellow Door: "front-right, mid distance". NE. Estimated pos: (1+2, 3+2) = (3, 5).
* From Plant (facing South): "front-left".
* **Basket:**
* From Yellow Door: "front-slight-right, slightly far". Slightly far is (4, 8]. Let's say 5 units. NNE. Estimated pos: (1+1, 3+5) = (2, 8).
* From Plant (facing East): "front-right".
* **Plant:**
* From Yellow Door: "front-slight-left, slightly far". NNW. Estimated pos: (1-1, 3+5) = (0, 8).
* From Basket (facing North): "front-left".

**Refining Positions:**
* **Yellow Door:** (1, 3).
* **Agent currently:** At `cap`, facing South (because I just rotated 90 clockwise from East).
* Previous step: Jumped to `cap`. Observed nothing facing East.
* Current step: Rotated 90 deg clockwise. Now facing South. Observed `yellow door` at front-right, mid distance.
* If Agent at `cap` (3, 5) faces South, `yellow door` at (1, 3) is dx=-2, dy=-2. Distance sqrt(8) ~ 2.8 (mid distance). Angle: atan2(-2, -2) = -135 (South-West). Relative to South (0 deg), this is Right-Front (45 deg right). This matches "front-right".
* So, Cap at (3, 5) and Yellow Door at (1, 3) works well.

* **Television:**
* From Yellow Door (1, 3) facing North: Front-Left.
* From Plant (0, 8) facing South: Front (South). So TV is at x=0?
* If TV is at (-1, 5), from Plant (0, 8) facing South, it is Front-Slight-Left or Front-Right?
* Let's check Plant pos. From Yellow Door (1, 3), Plant is Front-Slight-Left (NNW). If Plant is at (0, 8), angle is atan2(-1, 5) = -11 deg (slight left). Matches.
* From Plant (0, 8) facing South, TV at (-1, 5) is dx=-1, dy=-3. Angle relative to South: atan2(-1, -3). South is -y. Relative bearing: slightly right? No, South is Front. (-1, -3) is slightly right (Agent's right is West).
* Wait, Observation from Plant (facing South) said: TV is "front".
* This implies TV is roughly at same X as Plant. So TV x ~ 0.
* Let's place TV at (0, 5) or (-1, 5).
* Let's place Plant at (0, 8).
* Let's place Basket. From Yellow Door (1, 3), Basket is Front-Slight-Right (NNE). If Basket is at (2, 8), angle is atan2(1, 5) = 11 deg. Matches.
* From Plant (0, 8) facing East, Basket (2, 8) is Front. Matches.
* From Basket (2, 8) facing North, Plant (0, 8) is Left (West). Observation said "front-left". dx=-2, dy=0. Relative to North is West (Left). Front-Left bin is [-45, 0). -90 is Left. So maybe Basket is slightly South of Plant or Plant slightly North?
* If Basket is (2, 7) and Plant (0, 8). From Basket (N): Plant is (-2, 1). Angle atan2(-2, 1) = -63 deg. This is "Left". "Front-Left" is [-45, 0).
* Maybe Basket (2, 8) and Plant (0, 9)?
* Let's stick to simple integers.
* Let's update TV. From Plant (facing South), TV is Front. TV at (0, 5).
* Check TV from Yellow Door (1, 3): (0, 5) is dx=-1, dy=2. Angle atan2(-1, 2) = -26 deg. This is "front-left" ([-45, -22.5)). Perfect.
* Check Cap from Yellow Door (1, 3): (3, 5) is dx=2, dy=2. Angle 45 deg. "Front-Right" ((22.5, 45]). Perfect.

**Summary of Coordinates:**
* Agent: At `cap` (3, 5). Facing South.
* Yellow Door: (1, 3).
* Television: (0, 5). Facing? Seen "facing forward" from Plant (South). Means TV faces North? Or TV faces into room? Usually "facing forward" means looking at it, it faces you. If I am South of it looking North, it faces South. Wait. From Plant (South), I look South. TV is Front (South of me). So I look at TV's back? "Facing backward". The observation said "facing backward". So TV faces South (same as me).
* Let's check first observation of TV. From Yellow Door (North), TV "facing forward". I look North, TV is North of me. "Facing forward" means its front is towards me? So TV faces South.
* Observation from Plant (South): "facing backward". I look South. TV faces South. So I see its back. Consistent.
* So TV faces South.
* Cap: (3, 5). Facing? From Yellow Door (North): "facing right". I look North. Cap faces East?
* From Plant (South): "facing left". I look South. My Left is East. Cap faces East. Consistent.
* So Cap faces East.
* Basket: (2, 8).
* Plant: (0, 8).

**Final Map Content:**
* Agent: pos [3, 5], facing "south"
* yellow door: pos [1, 3]
* television: pos [0, 5], facing "south"
* cap: pos [3, 5], facing "east"
* basket: pos [2, 8]
* plant: pos [0, 8]

Wait, the prompt asks for "facing" if the object has it.
Doors usually align with walls. Yellow door on "front wall" of Room 1 (North wall). So it faces South/North.
Let's just list the objects.

Also, I haven't seen the Brown Door yet. It is not in the map.

One correction: `yellow door` observed from Room 1 (0,0) was "on front wall".
Pos (1, 3).
Wait, from (0,0) facing North, (1, 3) is dx=1, dy=3. Angle 18 deg. Front-slight-right. Correct.

Let's refine the coordinates to be safe integers.
Agent at `cap`.

FINAL ANSWER:
{
"agent": {"position": [3, 5], "facing": "south"},
"yellow door": {"position": [1, 3], "facing": "south"},
"television": {"position": [0, 5], "facing": "south"},
"cap": {"position": [3, 5], "facing": "east"},
"basket": {"position": [2, 8]},
"plant": {"position": [0, 8]}
}

THINK:
I need to construct a cognitive map of the environment based on my observations so far.

**Coordinate System:**
* Origin (0, 0) is my initial position in Room 1.
* North is +y, East is +x.

**Room 1:**
* **Initial Position:** (0, 0).
* **Yellow Door:**Observed from (0,0) facing North ...

{
  "agent": {
    "position": [
      3,
      5
    ],
    "facing": "south"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      3,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      8
    ]
  },
  "plant": {
    "position": [
      0,
      8
    ]
  }
}

{
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      5
    ],
    "facing": "south"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      2,
      5
    ],
    "facing": "south"
  }
}

THINK:
I am currently at the `cap` facing South (which corresponds to facing the South wall of Room 2).
I observe the `yellow door` at "front-right, mid distance".
Since I am facing South, "front" is South. "Right" is West. So "front-right" is South-West relative to me.
However, in the local frame:
- Origin: Agent (at `cap`).
- +y: Forward (South).
- +x: Right (West).
- -x: Left (East).
- -y: Backward (North).

Observation: "yellow door: front-right".
In standard bins: front-right is roughly 45 degrees to the right.
Let's approximate coordinates. "Mid distance" usually means 2-4 units. Let's say (x=2, y=2) in the local frame.
The door is "on front wall".
Wait, if I face South, the "front wall" is the South wall.
So the door is at the South wall.
Relative position: (+x, +y) quadrant.
Let's assign reasonable coordinates.
Object: "yellow door".
Position: [1, 2] or similar.
Facing: The door is "on front wall", meaning it faces me (North). In local frame (where +y is South), North is -y. So facing "-y".

Let's refine.
Agent at `cap` facing South.
Yellow door is "front-right".
Coordinate: [x, y]. Front is +y. Right is +x.
So x > 0, y > 0.
Let's say [1, 2].
Facing: The door is on the wall I'm facing. I'm facing South (+y). The door faces North (-y).

JSON:
{
"origin": "agent",
"objects": {
"yellow door": {"position": [1, 2], "facing": "-y"}
}
}

FINAL ANSWER:
{
"origin": "agent",
"objects": {
"yellow door": {"position": [1, 2], "facing": "-y"}
}
}

THINK:
I am currently at the `cap` facing South (which corresponds to facing the South wall of Room 2).
I observe the `yellow door` at "front-right, mid distance".
Since I am facing South, "front" is South. "Right" is West. So "front-right" is South-West relative to me.
However, in the local frame:
...

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        1,
        2
      ],
      "facing": "-y"
    }
  }
}

{
  "yellow door": {
    "position": [
      1,
      2
    ],
    "facing": "north"
  }
}

{
  "origin": "agent",
  "objects": {
    "yellow door": {
      "position": [
        1,
        2
      ],
      "facing": "-y"
    }
  }
}

THINK:
I am currently at the `cap` in Room 2 (the upper room in the map, indicated by the agent `*`). I have explored Room 2 extensively (North, West, East walls). I just rotated to face South and see the `yellow door` (the `+` connecting to the room below). The room below is Room 1.
The candidates are A, B, C, D, E, F located in Room 1 (the lower room).
The map shows Room 1 as the lower area. The `yellow door` connects Room 1 and Room 2.
I started in Room 1 at (0,0) facing North. I only looked North (saw yellow door) and jumped to it. I have NOT looked South, East, or West in Room 1.
Candidate A: Near the yellow door in Room 1. I likely saw this area when looking North from (0,0) or jumping to the door? No, A is to the right of the path.
Candidate B: Further right in Room 1. Unexplored.
Candidate C: Bottom left of Room 1. Unexplored.
Candidate D: Top right corner of Room 1. Unexplored.
Candidate E: Left side of Room 1. Unexplored.
Candidate F: Center/Left of Room 1. Unexplored.

Wait, I need to be precise.
I started at (0,0) facing North. FOV is 90 degrees (cone).
I saw `yellow door` at `front-slight-right`.
This means the door is roughly North-East from (0,0)? Or just North? The map shows the door centered on the top wall of Room 1.
My view cone from (0,0) facing North covers the central corridor to the door.
Points A and B are near the top right of Room 1. I might not have seen them if they are in the corners.
Points C, E are on the left/bottom-left. Definitely unobserved.
Point F is central-left. Might be unobserved.
Point D is top right corner. Unobserved.

Looking at the ASCII map provided:
Room 1 is the 5x5(ish) room at the bottom left.
My start was presumably near the bottom.
The agent `*` is in Room 2 (top room).
The `+` between them is the yellow door.
I am asked to select points in *unexplored/unobserved* regions.
Since I essentially skipped Room 1 (jumped to door immediately), most of Room 1 is unexplored, especially the sides and back (South) which I never faced.
A, B, D are on the East side of Room 1.
C, E, F are on the West/South side of Room 1.
I only saw the cone towards the door.
However, usually "unexplored" means areas I haven't seen.
I definitely haven't seen C, E.
F is likely unobserved.
A, B, D might be unobserved depending on the cone width, but given I only looked North once from (0,0), the corners are likely unseen.
Actually, the probe asks for "unexplored/unobserved".
Given I haven't been to Room 1's side areas, they are all candidates.
However, usually the "path" to the door is observed.
Let's look at the map again.
A, B are near the door on the right.
F is near the door on the left? No, F is further down.
D is top right corner.
E is left wall.
C is bottom left.
I will select all of them as I only did one Observe from (0,0) North. The FOV is 90 deg.
From (0,0) facing North, I see a triangle.
Points C (bottom left), E (left), F (center left), D (top right), B (right) are likely outside that initial narrow triangle or obscured.
Actually, let's select the ones definitely out of view.
C, E: Behind/Left. Unseen.
D, B: Right/Top Right. Unseen (probably).
A, F: Closer to the center line. Maybe seen?
But to be safe and rigorous, since I haven't explored Room 1 properly, I should mark them.
However, looking at the pattern, usually the "corners" and "behind" are the answer.
Let's select C, E, F, D, B, A. All of them.
Wait, maybe A and B are close to the door I observed?
I observed "yellow door". The door is at the wall.
A is adjacent to the door? No, A is further right.
Let's mark all points in Room 1 as unexplored except maybe the direct line.
But I can't distinguish precisely.
Let's assume the question implies "points in the room I haven't surveyed". I haven't surveyed Room 1.
I will select all.

Wait, let's look closer at the map.
Room 1 coordinates.
Start (0,0). North is Up.
Yellow door is at top of Room 1.
Candidates:
C: (1,1)? Bottom left.
E: (1,3)? Left wall.
F: (3,4)? Center left.
A: (5,4)? Center right.
B: (6,4)? Right.
D: (6,6)? Top right corner.
My start was likely (3,1) or something central? "Unless otherwise specified... origin (0,0)".
If (0,0) is bottom-left, and I faced North.
If I am at (0,0) facing North, I see a cone between -45 and +45 degrees from Y-axis.
X > Y (Right) is unseen? No, X=Y is 45 deg.
So points where x > y (East) or x < -y (impossible) are unseen?
Wait, (0,0) is bottom-left. Room 1 is from x=0 to x=6, y=0 to y=6.
If I am at (0,0), facing North (Y+).
Visible: Cone bounded by y=x (Right bound) and y=-x (Left bound).
Since x>=0, y>=0.
Visible area: y >= x. (Points to the North-West? No. North is Y+. Right is X+. 0 deg is North. +45 is North-East. -45 is North-West.)
So visible cone is between North-West and North-East.
i.e. |x| <= y.
So points where x > y are NOT visible (Too far right).
Points where x < -y (Too far left) - not applicable in 1st quadrant.
So points where x <= y are visible.
Let's check candidates.
Assume (0,0) is bottom-left corner of the room.
C is near (0,0). If I am at (0,0), I can't see C if C is (1,0) or (0,1)?
If I am at (0,0), I see objects.
But wait, the prompt says "current (initial) position is in room 1... treat your initial position as origin (0,0)".
So I am at (0,0).
Room 1 extends where?
Usually Room 1 contains the origin.
If the map shows Room 1 as the box, and `+` is at the top.
The candidates C, E, F are on the left. A, B, D on the right.
If (0,0) is centered bottom?
"Map ... (0,0) is at the bottom-left". This refers to the ASCII map coordinates?
The ASCII map has `#` borders.
Let's assume the map visualizes the layout relative to the map grid.
And the agent started at some position in Room 1.
If I started at bottom-center of Room 1 facing North.
Then Left (C, E) and Right (D, B) corners are likely blind spots.
I will select all Room 1 points: A, B, C, D, E, F.

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

THINK:
I am currently at the `cap` in Room 2 (the upper room in the map, indicated by the agent `*`). I have explored Room 2 extensively (North, West, East walls). I just rotated to face South and see the `yellow door` (the `+` connecting to the room below). The room below is Room 1.
The candidates ...

###############
###......######
###......######
###......######
###......######
###....*.######
###......######
######+########
#.....D########
#..F.AB#......#
#......#......#
#......#......#
#.E....+......#
#.C....#......#
########......#
###############

You rotated clockwise 90°. You observe:
• yellow door: front-right, mid distance, on front wall.
You have a maximum of 10 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]

You rotated clockwise 90°. You observe:
• yellow door: front-right, mid distance, on front wall.
You have a maximum of 10 exploration steps left.
Strictly follow this format:
THINK:
[Your thoughts on next step actions]
FINAL ANSWER:
Actions: [ ... ]...

I am at `cap` facing South.
`yellow door` is front-right.
I need to go to Room 1.
Action: JumpTo(yellow door).
After jumping, I will be at the door facing South (looking into Room 1).
I should Observe to find the `brown door` in Room 1.
Previously in Room 1 (start), I faced North and saw the yellow door. I didn't see anything else.
Now looking South from the yellow door, I will see the rest of Room 1.

I am at `cap` facing South.
`yellow door` is front-right.
I need to go to Room 1.
Action: JumpTo(yellow door).
After jumping, I will be at the door facing South (looking into Room 1).
I should Observe to find the `brown door` in Room 1.
Previously in Room 1 (start), I faced North and saw the yellow ...

THINK:
I have explored Room 2 and now returned to Room 1.
I am at the `yellow door`.
From `yellow door` (facing South), I observe:
- `scooter`: front-slight-right
- `backpack`: front-right
- `brown door`: front-slight-left (on left wall).

Global Frame Construction:
Origin (0,0) is initial pose in Room 1 facing North.
Yellow door was observed at "front-slight-right, mid distance" from (0,0) facing North.
Let's approximate coordinates.
"Mid distance" is (2, 4]. Let's say 3 units.
Front-slight-right means angle (0, 22.5]. Let's say ~15 degrees.
So (0,0) -> Yellow Door roughly at (1, 3) or (1, 4). Let's pick (1, 3).
Orientation at Yellow Door: I was facing North when I jumped. Then I jumped to `plant`, `basket`, `television`, `cap` and back to `yellow door`.
Wait, when I jumped to `yellow door` just now, I was at `cap` facing South. The `yellow door` was "front-right".
My orientation *at* the door depends on my last Jump.
Rule: "JumpTo(OBJ): Jump to the same position as the object or door. Your orientation does NOT change."
I was at `cap` facing South. I jumped to `yellow door`. So I am at `yellow door` facing South.
Observation matches: "scooter: front-slight-right", "backpack: front-right", "brown door: front-slight-left".
Facing South, "Front" is South. Left is East. Right is West.
Wait.
South is -Y.
Front-slight-left (from South) -> South-East?
No. Facing South.
Front = South.
Left = East.
Right = West.
"Front-slight-left" -> South turning towards East -> South-East.
"Front-slight-right" -> South turning towards West -> South-West.

Brown Door is "front-slight-left, on left wall".
If I face South, Left is East.
So Brown Door is roughly South-East.
Wait.
Room 1 is where I started at (0,0).
From (0,0) facing North, Yellow Door was Front-Right (North-East).
If Yellow Door is at (1, 3).
Facing South from (1, 3):
- Brown Door is Front-Left (South-East).
This places Brown Door at e.g. (2, 1).
- Scooter is Front-Slight-Right (South-West). e.g. (0, 1).
- Backpack is Front-Right (South-West/West). e.g. (-1, 1).

Wait, "brown door ... on left wall".
If I face South, Left wall is the East wall of the room.
This makes sense. Brown door leads to Room 3.
Room 2 objects:
Yellow Door is the connection.
From Yellow Door (facing North into Room 2):
- TV: Front-Left (North-West)
- Cap: Front-Right (North-East)
- Basket: Front-Slight-Right (Further North-East)
- Plant: Front-Slight-Left (Further North-West)

Let's assign coords.
Yellow Door: (1, 3).
Room 2 is North of Room 1.
TV: (-2, 6)
Cap: (4, 6)
Basket: (3, 9)
Plant: (-1, 9)

Room 1 objects:
Brown Door: South-East of Yellow Door. Say (4, 1).
Scooter: South-West of Yellow Door. Say (-1, 0).
Backpack: South-West. Say (-2, 0).
Initial pos: (0,0).

Let's refine.
Initial (0,0) facing N.
Yellow Door: Front-Right (NE). Mid distance (say 3m). Pos approx (1, 3).
At Yellow Door facing S:
Brown Door: Front-Left (SE). Slightly Far (4-8m).
If YD is at (1,3), SE is (1+dx, 3-dy).
Let's say (4, 0).
Scooter: Front-Slight-Right (SW). Slightly Far.
Backpack: Front-Right (SW/W). Slightly Far.

Current Position: at `yellow door`, facing South.
Agent: {"position": [1, 3], "facing": "south"} (Approx coords).

Wait, Brown Door connects to Room 3.
I haven't visited Room 3.
Brown Door is "on left wall" (East wall of Room 1).
My goal is to minimize cost and build a map.
I need to query if uncertain, but I have reasonable estimates.
I just need to output the map.
I should include all observed objects.
Room 1: scooter, backpack, brown door.
Room 2: television, cap, basket, plant.
Connectors: yellow door, brown door.

I'll use approximate integers.
Yellow Door: (0, 3).
TV: (-3, 6).
Cap: (3, 6).
Plant: (-2, 9).
Basket: (2, 9).
From Yellow Door (0,3) facing South:
Brown Door (Front-Left -> SE): (3, 0).
Scooter (Front-Right -> SW): (-3, 0).
Backpack (Front-Right -> SW): (-4, 1).
Initial (0,0).

Let's normalize.
Agent at Yellow Door.
Let's stick to the relative positions.

FINAL ANSWER:
```json
{
"agent": {"position": [1, 3], "facing": "south"},
"yellow door": {"position": [1, 3], "facing": "south"},
"television": {"position": [-2, 6], "facing": "west"},
"cap": {"position": [4, 6], "facing": "east"},
"basket": {"position": [3, 9], "facing": "north"},
"plant": {"position": [-1, 9], "facing": "south"},
"scooter": {"position": [-2, 0], "facing": "west"},
"backpack": {"position": [-3, 0], "facing": "north"},
"brown door": {"position": [4, 1], "facing": "east"}
}
```

THINK:
I have explored Room 2 and now returned to Room 1.
I am at the `yellow door`.
From `yellow door` (facing South), I observe:
- `scooter`: front-slight-right
- `backpack`: front-right
- `brown door`: front-slight-left (on left wall).

Global Frame Construction:
Origin (0,0) is initial pose in R...

{
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  },
  "television": {
    "position": [
      -2,
      6
    ],
    "facing": "west"
  },
  "cap": {
    "position": [
      4,
      6
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      3,
      9
    ],
    "facing": "north"
  },
  "plant": {
    "position": [
      -1,
      9
    ],
    "facing": "south"
  },
  "scooter": {
    "position": [
      -2,
      0
    ],
    "facing": "west"
  },
  "backpack": {
    "position": [
      -3,
      0
    ],
    "facing": "north"
  },
  "brown door": {
    "position": [
      4,
      1
    ],
    "facing": "east"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  }
}

{
  "scooter": {
    "position": [
      0,
      -3
    ],
    "facing": "east"
  },
  "television": {
    "position": [
      0,
      5
    ],
    "facing": "north"
  },
  "chair": {
    "position": [
      6,
      -3
    ],
    "facing": "south"
  },
  "shoes": {
    "position": [
      -4,
      -1
    ],
    "facing": "south"
  },
  "cap": {
    "position": [
      2,
      5
    ],
    "facing": "east"
  },
  "toilet": {
    "position": [
      8,
      -1
    ],
    "facing": "east"
  },
  "backpack": {
    "position": [
      -4,
      -3
    ],
    "facing": "south"
  },
  "wine": {
    "position": [
      -3,
      1
    ],
    "facing": "east"
  },
  "basket": {
    "position": [
      2,
      7
    ],
    "facing": "east"
  },
  "table": {
    "position": [
      4,
      -3
    ],
    "facing": "east"
  },
  "plant": {
    "position": [
      0,
      9
    ],
    "facing": "east"
  },
  "bike": {
    "position": [
      6,
      1
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      2,
      -2
    ],
    "facing": "east"
  },
  "yellow door": {
    "position": [
      1,
      3
    ],
    "facing": "north"
  },
  "agent": {
    "position": [
      1,
      3
    ],
    "facing": "south"
  }
}

THINK:
I am currently located at the `yellow door`, facing South (into Room 1).
I observe:
- `scooter`: front-slight-right, slightly far, facing left.
- `backpack`: front-right, slightly far, facing forward.
- `brown door`: front-slight-left, slightly far, on left wall.

Coordinates relative to agent (facing +y):
- Agent is at (0,0).
- `scooter`: "front-slight-right" means roughly (+x, +y). "Slightly far" is (4,8]. Let's estimate (2, 5). Facing "left" means facing -x (relative to agent).
- `backpack`: "front-right" means (+x, +y), more x than scooter. Let's estimate (4, 4). Facing "forward" means facing +y (relative to agent).
- `brown door`: "front-slight-left" means (-x, +y). "Slightly far" is (4,8]. Let's estimate (-2, 5). It is on the "left wall", so facing right (+x relative to agent). Wait, "on left wall" usually implies the door faces into the room from the left wall, so it faces +x relative to the room, or relative to me? The door itself is an opening. Usually doors on walls are described by the wall they are on. If it's on the left wall, it's to my left.

Let's construct the JSON.
Distance "slightly far" is 4-8m.
`front-slight-right`: angle (0, 22.5]. 5m distance -> x ~ 1-2, y ~ 4-5.
`front-right`: angle (22.5, 45]. 5m distance -> x ~ 3-4, y ~ 3-4.
`front-slight-left`: angle [-22.5, 0). 5m distance -> x ~ -1 to -2, y ~ 4-5.

Scooter facing "left": Since I face South, "left" is East. In local frame (+y is South), "left" is +x (East). Wait.
Local frame: +y is Agent's forward (South). +x is Agent's right (West). -x is Agent's left (East).
Wait, standard local frame:
Forward = +y.
Right = +x.
Left = -x.

Observed:
- `scooter`: front-slight-right -> (+x, +y). Facing "left". In local frame, left is -x. So facing "-x".
- `backpack`: front-right -> (+x, +y). Facing "forward". In local frame, forward is +y. So facing "+y".
- `brown door`: front-slight-left -> (-x, +y). On "left wall". Wall position isn't facing direction, but usually implies orientation. If I am facing South, left is East. So the wall is on the East. The door is on the East wall. So the door faces West (into the room). My Right is West. My Left is East.
Wait.
Agent faces South.
Right is West.
Left is East.
`brown door` is front-slight-left -> In my Left sector (East side).
"On left wall" -> On the East wall.
Orientation of door: usually perpendicular to wall. If on East wall, faces West (my Right).
Let's assume "on left wall" is a location description. The door object doesn't have a specific facing listed like "facing left", it says "on left wall". I will omit facing if not explicitly "facing X" or infer if possible. The instructions say "Gate's orientation: report wall position". I'll put position relative to me.

JSON content:
Origin: agent.
Objects: scooter, backpack, brown door.
Positions:
Scooter: (2, 6) (slightly far, slight right). Facing: "-x" (left).
Backpack: (5, 5) (slightly far, right). Facing: "+y" (forward).
Brown door: (-2, 6) (slightly far, slight left). Facing: Not specified as "facing X", but "on left wall". I'll omit facing or put null? The instructions say "MUST include facing key if the object has facing direction". The observation says "facing left" for scooter, "facing forward" for backpack. For door it says "on left wall". I will interpret "on left wall" as the facing or just omit if uncertain. But actually, doors usually have orientation. If it's on the left wall (relative to me looking South), it's the East wall. So it faces West (my Right, +x).
However, for the local map, I should stick to what is explicitly given or standard coordinates.
Let's just use approximate coordinates.

FINAL ANSWER:
```json
{
"origin": "agent",
"objects": {
"scooter": {"position": [2, 6], "facing": "-x"},
"backpack": {"position": [4, 4], "facing": "+y"},
"brown door": {"position": [-2, 6], "facing": "+x"}
}
}
```

THINK:
I am currently located at the `yellow door`, facing South (into Room 1).
I observe:
- `scooter`: front-slight-right, slightly far, facing left.
- `backpack`: front-right, slightly far, facing forward.
- `brown door`: front-slight-left, slightly far, on left wall.

Coordinates relative to agen...

{
  "origin": "agent",
  "objects": {
    "scooter": {
      "position": [
        2,
        6
      ],
      "facing": "-x"
    },
    "backpack": {
      "position": [
        4,
        4
      ],
      "facing": "+y"
    },
    "brown door": {
      "position": [
        -2,
        6
      ],
      "facing": "+x"
    }
  }
}

{
  "backpack": {
    "position": [
      5,
      6
    ],
    "facing": "south"
  },
  "scooter": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      -1,
      5
    ],
    "facing": "east"
  }
}

{
  "origin": "agent",
  "objects": {
    "scooter": {
      "position": [
        2,
        6
      ],
      "facing": "-x"
    },
    "backpack": {
      "position": [
        4,
        4
      ],
      "facing": "+y"
    },
    "brown door": {
      "position": [
        -2,
        6
      ],
      "facing": "+x"
    }
  }
}

{
  "backpack": {
    "position": [
      5,
      6
    ],
    "facing": "south"
  },
  "scooter": {
    "position": [
      1,
      6
    ],
    "facing": "east"
  },
  "brown door": {
    "position": [
      -1,
      5
    ],
    "facing": "east"
  }
}

THINK:
I have just jumped to the `yellow door` and I am looking South into Room 1.
I see:
- `scooter`: front-slight-right
- `backpack`: front-right
- `brown door`: front-slight-left

My current position is at the `yellow door` which is between Room 1 (South) and Room 2 (North).
In the provided map:
The agent `*` is at the doorway between the top room (Room 2) and the bottom room (Room 1).
The map shows Room 2 (top) and Room 1 (bottom).
The agent is facing South (down).
My FOV is 90 degrees forward (South).
Visible area:
- To the front-left (South-East in map coordinates since I face South? No. South is -Y. Left is East. Right is West. Wait.
- Facing South (down in map).
- Left is East (Right in map).
- Right is West (Left in map).
- Front is South (Down in map).

Let's check the labels relative to my view.
- `brown door`: front-slight-left. If I face South, Left is East. So Brown Door is South-East?
- Wait, "on left wall". If I face South, my Left is East. So the East wall of Room 1 has the brown door?
- Let's look at the map. The map has `*` at the door. Below it is Room 1.
- Points D, F, B, E, A, C are in Room 1.
- Point A is roughly central.
- Points B, E are on the West side (left side of map).
- Points D is West. F is ... well, D and F are near the door.
- Point C is South-East.
- The "brown door" is "front-slight-left".
- If I face South (down), Front-Left is South-East.
- "on left wall". Left wall relative to me (facing South) is the East wall of the room.
- So the brown door is likely on the East wall of Room 1.
- Looking at the map, there is a `+` symbol on the East wall? No, the `+` is on the bottom wall? Or right wall?
- Wait, look at the ASCII map.
- Room 1 is the bottom one.
- `*` is at the door connecting Room 1 and 2.
- `+` is shown on the bottom-ish wall? Or is that a door?
- Let's look closer at the ASCII.
`#......+......#` row.
Wait, `+` usually means door.
The map shows a `+` at (x,y) roughly centered horizontally, low down.
Is that the brown door?
If so, it's on the South wall?
But observation says "front-slight-left, on left wall".
Facing South. Left is East.
Maybe my orientation interpretation is wrong.

Let's re-evaluate "Left/Right" vs "West/East".
Initial pose: Room 1 (0,0), facing North.
I jumped to yellow door (North).
I am now at yellow door facing South (Rotated 180 at Plant, jumped to TV, rotated, jumped to Cap, rotated, jumped to Yellow Door. Wait.
At Cap, I faced South. Jumped to Yellow Door. So I am facing South.
South is Down on the map.
Left is East (Right on map).
Right is West (Left on map).
"front-slight-left" -> South-East.
"on left wall" -> East wall.

So I see the East part of Room 1.
My FOV covers the South-East cone.

Candidates:
- A: Central Room 1. Likely visible or close.
- B: West wall. Behind my right shoulder? No. Front-Right is West. B is West. "backpack" is front-right. So I see West.
- C: South-East corner. "brown door" is front-slight-left.
- D: North-West corner (near door).
- E: West wall.
- F: North-East corner (near door).

Let's check the Fog Probe question: "Select the points that are located in unexplored/unobserved regions."
I just Observed from the yellow door facing South.
I see:
- `scooter` (front-slight-right -> South-West).
- `backpack` (front-right -> West).
- `brown door` (front-slight-left -> South-East).

My FOV (90 degrees, South) covers South-West to South-East.
The area immediately to my East and West (90 degrees to side) is not visible.
The area behind me (North) is Room 2 (Observed).

Points in Room 1:
- D: Near the door, to the West. My FOV is South-West to South-East. D is likely to the side (West) or slightly behind the 45 degree line?
- If D is (x < agent_x, y ~ agent_y), it's to my Right. Not Front-Right. Front-Right is (x < agent_x, y < agent_y).
- If D is "near", it might be outside FOV if it's strictly West.
- "backpack" is Front-Right. Backpack is usually an object, not a point.
- Let's assume the cone covers the central part (A), the "scooter" area (SW), the "backpack" area (W/SW), and "brown door" area (SE).
- F: Near the door, to the East. Likely outside FOV (to the Left).
- B: West wall, further South. Likely visible (near backpack?).
- E: West wall, further South. Likely visible.
- C: South-East. Near brown door? Likely visible.
- A: Central. Definitely visible.

Unobserved regions:
- The corners immediately to the left/right of the door might be missed if the FOV is strictly 45 deg to 45 deg.
- F is very close to the wall/door on the East side.
- D is very close to the wall/door on the West side.
- C is deep South-East. Visible.
- B, E are West. Visible.

Actually, let's look at the labels again.
`D` and `F` are on the row just below the agent `*`.
`*` is at `######*########`.
Row below is `#.D..F.########`.
Wait, `D` is separated by `.`. `F` is separated by `.`.
They are very close to the agent Y-level.
If I face South, my FOV starts from the agent position.
Objects at Y-1 (immediate front) are visible.
Objects at Y-0 (same row) are not.
D and F are at Y-1?
The map rows:
Row N: `######*########` (Agent)
Row N-1: `#.D..F.########`
D is at X-2 relative to agent? F is at X+1?
If I look South, the cone expands.
At distance 1, width is small.
If D and F are to the side, they might be missed.
"backpack" is front-right. "scooter" is front-slight-right.
"brown door" is front-slight-left.
This implies I see objects to the right and left.
However, D and F are "high up" in Room 1 (Northern part of Room 1).
Usually, the cone of vision misses the corners near the agent.
So D and F are likely Unobserved.

Points A, B, C, E are further South.
A is central. Visible.
B, E are West. "backpack" is Front-Right. I see that area.
C is South-East. "brown door" is Front-Slight-Left. I see that area.

So candidates for Unexplored: D, F.

Let's check B and E.
Backpack is "front-right".
Scooter is "front-slight-right".
I see the West side.
So B and E (West side) should be covered.

What about C?
Brown door is "front-slight-left".
This covers the East side.
So C should be covered.

Conclusion: D and F are the most likely to be unobserved because they are in the top corners of Room 1, which are often blind spots when standing at the door looking in.

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

THINK:
I have just jumped to the `yellow door` and I am looking South into Room 1.
I see:
- `scooter`: front-slight-right
- `backpack`: front-right
- `brown door`: front-slight-left

My current position is at the `yellow door` which is between Room 1 (South) and Room 2 (North).
In the provided map:
...

###############
###......######
###......######
###......######
###......######
###......######
###......######
######*########
#.D..F.########
#......#......#
#BE....#......#
#....A.#......#
#......+......#
#.....C#......#
########......#
###############