[TASK]
You'll see a story about object placement. Each story involves four components: Agents, Objects, Rooms, and Containers. Given a question about an (agent, object) pair, your task is to track the locations and beliefs in stories about object placement asked in the question.

[APPROACH]
You will solve the problem by tracking the location of the agent, location of the object, and the agent's belief of the object.
1. Initial Setup: set up agent's starting location, object's starting location, agent's initial belief on the object's location. Note that if an agent does not see an object at the start, their belief on the object is None.
2. Then, track step-by-step:
* If a step involves that the agent moves to another room, leaves a room, or enters a room, you should update the agent's location. Note that if the agent leaves the current room but hasn't entered another room, the agent's location is None.
* If a step involves the object of interest moving, you should update the object's location.
* To keep track of the agent's belief on the object: If the agent and the object are in the same room, the agent can see the object, so the agent's belief will reflect the true location of the object. If the agent cannot see the object (the agent is in a different room or not in any rooms), the agent's belief will remain unchanged until the agent sees the object again.
3. Format your output exactly as shown in example answers below.

[EXAMPLE STORY1]
Step 0: Catherine is in the patio; Kristin is in the patio; the pencil sharpener is on the sauna's table; the thread spool is on the sauna's table.
Step 1: Catherine moves to the sauna.
Step 2: Catherine moves to the patio.
Step 3: Catherine moves to the sauna.
Step 4: Catherine moves the pencil sharpener to the sauna's nightstand.
Step 5: Catherine moves to the patio.
Step 6: Kristin moves to the sauna.
Step 7: Catherine moves to the sauna.
Step 8: Kristin leaves the room he was in.
Step 9: Catherine moves the thread spool to the sauna's nightstand.
Step 10: Kristin enters the patio.

[EXAMPLE QUESTION1]
Where does Catherine believe the thread spool is?

[EXAMPLE ANSWER1]
Catherine's belief on the thread spool:
- Step 0: (initial state) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: None}
- Step 1: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 2: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 3: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 4: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 5: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 6: (Catherine location unchanged; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 7: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 8: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 9: (Catherine location unchanged; thread spool location changed) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
- Step 10: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
Final Answer: the sauna's nightstand

[EXAMPLE STORY2]
Step 0: Kathryn is in the storage room; Mitchell is in the storage room; the rubber band is on the patio's coffee table; the fuse is on the patio's coffee table.
Step 1: Kathryn moves to the patio.
Step 2: Kathryn moves to the storage room, and moves the fuse to the storage room's ledge.
Step 3: Kathryn moves the fuse to the storage room's coffee table.
Step 4: Mitchell leaves the room he was in.
Step 5: Kathryn moves the fuse to the storage room's ledge.
Step 6: Mitchell enters the storage room.
Step 7: Kathryn moves to the patio, and moves the fuse to the patio's ledge.
Step 8: Kathryn moves the rubber band to the patio's ledge.
Step 9: Kathryn moves to the storage room, and moves the rubber band to the storage room's ledge.
Step 10: Mitchell moves the rubber band to the storage room's coffee table.

[EXAMPLE QUESTION2]
Where does Kathryn believe the fuse is?

[EXAMPLE ANSWER2]
Kathryn's belief on the fuse:
- Step 0: (initial state) {Kathryn location: storage room; fuse location: patio's coffee table; Kathryn sees fuse: False; Kathryn's belief on fuse: None}
- Step 1: (Kathryn location changed; fuse location unchanged) {Kathryn location: patio; fuse location: patio's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's coffee table}
- Step 2: (Kathryn location changed; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 3: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 4: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 5: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 6: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 7: (Kathryn location changed; fuse location changed) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 8: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 9: (Kathryn location changed; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
- Step 10: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
Final Answer: the patio's ledge

[PROBLEM]
Read the following story and answer the question. Please carefully follow the approach and examples provided above when solving the problem. Remember that the output format should follow the examples.

[STORY]
Step 0: Donna is in the patio; Caroline is in the mudroom; the pencil case is on the patio's buffet; the eyedrop bottle is on the patio's table.
Step 1: Donna leaves the room he was in.
Step 2: Caroline moves to the patio.
Step 3: Donna enters the patio.
Step 4: Caroline moves to the mudroom.
Step 5: Donna moves the pencil case to the patio's table.
Step 6: Donna moves to the mudroom.
Step 7: Donna moves to the patio.
Step 8: Donna moves to the mudroom, and moves the eyedrop bottle to the mudroom's buffet.
Step 9: Donna moves to the patio.
Step 10: Caroline moves the eyedrop bottle to the mudroom's table.
Step 11: Donna moves the pencil case to the patio's buffet.
Step 12: Caroline moves to the patio.
Step 13: Donna moves to the mudroom, and moves the pencil case to the mudroom's table.
Step 14: Donna moves to the patio, and moves the eyedrop bottle to the patio's buffet.
Step 15: Donna moves to the mudroom.
Step 16: Caroline moves to the mudroom.
Step 17: Donna moves the pencil case to the mudroom's buffet.
Step 18: Caroline moves to the patio.
Step 19: Donna moves the pencil case to the mudroom's table.
Step 20: Caroline moves to the mudroom.
Step 21: Donna moves the pencil case to the mudroom's buffet.
Step 22: Caroline leaves the room he was in.
Step 23: Donna moves to the patio, and moves the pencil case to the patio's buffet.
Step 24: Caroline enters the mudroom.
Step 25: Donna leaves the room he was in.
Step 26: Caroline moves to the patio.
Step 27: Donna enters the patio.
Step 28: Caroline moves the eyedrop bottle to the patio's table.
Step 29: Donna moves the eyedrop bottle to the patio's buffet.
Step 30: Caroline leaves the room he was in.
Step 31: Donna moves to the mudroom, and moves the eyedrop bottle to the mudroom's buffet.
Step 32: Caroline enters the mudroom.
Step 33: Donna moves to the patio.
Step 34: Caroline moves to the patio.
Step 35: Donna moves the pencil case to the patio's table.
Step 36: Caroline moves to the mudroom, and moves the pencil case to the mudroom's table.
Step 37: Donna moves to the mudroom.
Step 38: Caroline moves to the patio, and moves the eyedrop bottle to the patio's table.
Step 39: Donna moves the pencil case to the mudroom's buffet.
Step 40: Caroline moves the eyedrop bottle to the patio's buffet.

[QUESTION]
Where does Caroline believe the pencil case is?

[YOUR ANSWER]

Caroline's belief on the pencil case:
- Step 0: (initial state) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: None}
- Step 1: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: None}
- Step 2: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 3: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 4: (Caroline location changed; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 5: (Caroline location unchanged; pencil case location changed) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 6: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 7: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 8: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 9: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 10: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 11: (Caroline location unchanged; pencil case location changed) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 12: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 13: (Caroline location unchanged; pencil case location changed) {Caroline location: patio; pencil case location: mudroom's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 14: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: mudroom's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 15: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: mudroom's table; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 16: (Caroline location changed; pencil case location unchanged) {Caroline location: mudroom; pencil case location: mudroom's table; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's table}
- Step 17: (Caroline location unchanged; pencil case location changed) {Caroline location: mudroom; pencil case location: mudroom's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's buffet}
- Step 18: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: mudroom's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 19: (Caroline location unchanged; pencil case location changed) {Caroline location: patio; pencil case location: mudroom's table; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 20: (Caroline location changed; pencil case location unchanged) {Caroline location: mudroom; pencil case location: mudroom's table; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's table}
- Step 21: (Caroline location unchanged; pencil case location changed) {Caroline location: mudroom; pencil case location: mudroom's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's buffet}
- Step 22: (Caroline location changed; pencil case location unchanged) {Caroline location: None; pencil case location: mudroom's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 23: (Caroline location unchanged; pencil case location changed) {Caroline location: None; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 24: (Caroline location changed; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 25: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's buffet}
- Step 26: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 27: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 28: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 29: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 30: (Caroline location changed; pencil case location unchanged) {Caroline location: None; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 31: (Caroline location unchanged; pencil case location unchanged) {Caroline location: None; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 32: (Caroline location changed; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 33: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: patio's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: patio's buffet}
- Step 34: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: patio's buffet; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's buffet}
- Step 35: (Caroline location unchanged; pencil case location changed) {Caroline location: patio; pencil case location: patio's table; Caroline sees pencil case: True; Caroline's belief on pencil case: patio's table}
- Step 36: (Caroline location changed; pencil case location changed) {Caroline location: mudroom; pencil case location: mudroom's table; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's table}
- Step 37: (Caroline location unchanged; pencil case location unchanged) {Caroline location: mudroom; pencil case location: mudroom's table; Caroline sees pencil case: True; Caroline's belief on pencil case: mudroom's table}
- Step 38: (Caroline location changed; pencil case location unchanged) {Caroline location: patio; pencil case location: mudroom's table; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's table}
- Step 39: (Caroline location unchanged; pencil case location changed) {Caroline location: patio; pencil case location: mudroom's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's table}
- Step 40: (Caroline location unchanged; pencil case location unchanged) {Caroline location: patio; pencil case location: mudroom's buffet; Caroline sees pencil case: False; Caroline's belief on pencil case: mudroom's table}
Final Answer: the mudroom's table

Question: Where does Caroline believe the pencil case is?

Agents: [Donna, Caroline].
Objects: [the pencil case, the eyedrop bottle].
Rooms: [the patio, the mudroom].
Containers: [the patio's buffet, the patio's table, the mudroom's buffet, the mudroom's table]


[TASK]
You'll see a story about object placement. Each story involves four components: Agents, Objects, Rooms, and Containers. Given a question about an (agent, object) pair, your task is to track the locations and beliefs in stories about object placement asked in the question.

[APPROACH]
You will solve the problem by tracking the location of the agent, location of the object, and the agent's belief of the object.
1. Initial Setup: set up agent's starting location, object's starting location, agent's initial belief on the object's location. Note that if an agent does not see an object at the start, their belief on the object is None.
2. Then, track step-by-step:
* If a step involves that the agent moves to another room, leaves a room, or enters a room, you should update the agent's location. Note that if the agent leaves the current room but hasn't entered another room, the agent's location is None.
* If a step involves the object of interest moving, you should update the object's location.
* To keep track of the agent's belief on the object: If the agent and the object are in the same room, the agent can see the object, so the agent's belief will reflect the true location of the object. If the agent cannot see the object (the agent is in a different room or not in any rooms), the agent's belief will remain unchanged until the agent sees the object again.
3. Format your output exactly as shown in example answers below.

[EXAMPLE STORY1]
Step 0: Catherine is in the patio; Kristin is in the patio; the pencil sharpener is on the sauna's table; the thread spool is on the sauna's table.
Step 1: Catherine moves to the sauna.
Step 2: Catherine moves to the patio.
Step 3: Catherine moves to the sauna.
Step 4: Catherine moves the pencil sharpener to the sauna's nightstand.
Step 5: Catherine moves to the patio.
Step 6: Kristin moves to the sauna.
Step 7: Catherine moves to the sauna.
Step 8: Kristin leaves the room he was in.
Step 9: Catherine moves the thread spool to the sauna's nightstand.
Step 10: Kristin enters the patio.

[EXAMPLE QUESTION1]
Where does Catherine believe the thread spool is?

[EXAMPLE ANSWER1]
Catherine's belief on the thread spool:
- Step 0: (initial state) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: None}
- Step 1: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 2: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 3: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 4: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 5: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 6: (Catherine location unchanged; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 7: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 8: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 9: (Catherine location unchanged; thread spool location changed) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
- Step 10: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
Final Answer: the sauna's nightstand

[EXAMPLE STORY2]
Step 0: Kathryn is in the storage room; Mitchell is in the storage room; the rubber band is on the patio's coffee table; the fuse is on the patio's coffee table.
Step 1: Kathryn moves to the patio.
Step 2: Kathryn moves to the storage room, and moves the fuse to the storage room's ledge.
Step 3: Kathryn moves the fuse to the storage room's coffee table.
Step 4: Mitchell leaves the room he was in.
Step 5: Kathryn moves the fuse to the storage room's ledge.
Step 6: Mitchell enters the storage room.
Step 7: Kathryn moves to the patio, and moves the fuse to the patio's ledge.
Step 8: Kathryn moves the rubber band to the patio's ledge.
Step 9: Kathryn moves to the storage room, and moves the rubber band to the storage room's ledge.
Step 10: Mitchell moves the rubber band to the storage room's coffee table.

[EXAMPLE QUESTION2]
Where does Kathryn believe the fuse is?

[EXAMPLE ANSWER2]
Kathryn's belief on the fuse:
- Step 0: (initial state) {Kathryn location: storage room; fuse location: patio's coffee table; Kathryn sees fuse: False; Kathryn's belief on fuse: None}
- Step 1: (Kathryn location changed; fuse location unchanged) {Kathryn location: patio; fuse location: patio's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's coffee table}
- Step 2: (Kathryn location changed; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 3: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 4: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 5: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 6: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 7: (Kathryn location changed; fuse location changed) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 8: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 9: (Kathryn location changed; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
- Step 10: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
Final Answer: the patio's ledge

[PROBLEM]
Read the following story and answer the question. Please carefully follow the approach and examples provided above when solving the problem. Remember that the output format should follow the examples.

[STORY]
Step 0: Christine is in the garage; Jonathan is in the garage; the eyedrop bottle is on the garage's coffee table; the rubber band is on the garage's ledge.
Step 1: Christine moves to the library.
Step 2: Jonathan moves the eyedrop bottle to the garage's ledge.
Step 3: Jonathan moves to the library.
Step 4: Jonathan moves to the garage.
Step 5: Jonathan moves the rubber band to the garage's coffee table.
Step 6: Jonathan leaves the room he was in.
Step 7: Christine moves to the garage.
Step 8: Jonathan enters the library.
Step 9: Christine leaves the room he was in.
Step 10: Jonathan moves to the garage.
Step 11: Christine enters the library.
Step 12: Jonathan moves to the library.
Step 13: Christine moves to the garage.
Step 14: Christine moves the eyedrop bottle to the garage's coffee table.
Step 15: Christine moves to the library.
Step 16: Jonathan moves to the garage.
Step 17: Christine moves to the garage.
Step 18: Jonathan leaves the room he was in.
Step 19: Christine moves to the library, and moves the rubber band to the library's ledge.
Step 20: Jonathan enters the garage.
Step 21: Christine moves to the garage, and moves the rubber band to the garage's coffee table.
Step 22: Jonathan leaves the room he was in.
Step 23: Christine moves the eyedrop bottle to the garage's ledge.
Step 24: Jonathan enters the garage.
Step 25: Christine moves to the library, and moves the eyedrop bottle to the library's coffee table.
Step 26: Jonathan moves the rubber band to the garage's ledge.
Step 27: Christine moves to the garage.
Step 28: Jonathan moves to the library, and moves the rubber band to the library's ledge.
Step 29: Christine moves to the library.
Step 30: Jonathan leaves the room he was in.
Step 31: Christine leaves the room he was in.
Step 32: Jonathan enters the library.
Step 33: Christine enters the garage.
Step 34: Jonathan moves the eyedrop bottle to the library's ledge.
Step 35: Christine moves to the library.
Step 36: Jonathan moves the eyedrop bottle to the library's coffee table.
Step 37: Christine moves to the garage.
Step 38: Jonathan leaves the room he was in.
Step 39: Christine moves to the library.
Step 40: Jonathan enters the garage.

[QUESTION]
Where does Christine believe the eyedrop bottle is?

[YOUR ANSWER]

Christine's belief on the eyedrop bottle:
- Step 0: (initial state) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 1: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 2: (Christine location unchanged; eyedrop bottle location changed) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 3: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 4: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 5: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 6: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 7: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's ledge}
- Step 8: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's ledge}
- Step 9: (Christine location changed; eyedrop bottle location unchanged) {Christine location: None; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's ledge}
- Step 10: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: None; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's ledge}
- Step 11: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's ledge}
- Step 12: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's ledge}
- Step 13: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's ledge}
- Step 14: (Christine location unchanged; eyedrop bottle location changed) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 15: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 16: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 17: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 18: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 19: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 20: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 21: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 22: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's coffee table}
- Step 23: (Christine location unchanged; eyedrop bottle location changed) {Christine location: garage; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's ledge}
- Step 24: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: garage's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: garage's ledge}
- Step 25: (Christine location changed; eyedrop bottle location changed) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 26: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 27: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 28: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 29: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 30: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 31: (Christine location changed; eyedrop bottle location unchanged) {Christine location: None; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 32: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: None; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 33: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 34: (Christine location unchanged; eyedrop bottle location changed) {Christine location: garage; eyedrop bottle location: library's ledge; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 35: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's ledge; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's ledge}
- Step 36: (Christine location unchanged; eyedrop bottle location changed) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 37: (Christine location changed; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 38: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: garage; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: False; Christine's belief on eyedrop bottle: library's coffee table}
- Step 39: (Christine location changed; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
- Step 40: (Christine location unchanged; eyedrop bottle location unchanged) {Christine location: library; eyedrop bottle location: library's coffee table; Christine sees eyedrop bottle: True; Christine's belief on eyedrop bottle: library's coffee table}
Final Answer: the library's coffee table

Question: Where does Christine believe the eyedrop bottle is?

Agents: [Christine, Jonathan].
Objects: [the eyedrop bottle, the rubber band].
Rooms: [the garage, the library].
Containers: [the garage's ledge, the garage's coffee table, the library's ledge, the library's coffee table]


[TASK]
You'll see a story about object placement. Each story involves four components: Agents, Objects, Rooms, and Containers. Given a question about an (agent, object) pair, your task is to track the locations and beliefs in stories about object placement asked in the question.

[APPROACH]
You will solve the problem by tracking the location of the agent, location of the object, and the agent's belief of the object.
1. Initial Setup: set up agent's starting location, object's starting location, agent's initial belief on the object's location. Note that if an agent does not see an object at the start, their belief on the object is None.
2. Then, track step-by-step:
* If a step involves that the agent moves to another room, leaves a room, or enters a room, you should update the agent's location. Note that if the agent leaves the current room but hasn't entered another room, the agent's location is None.
* If a step involves the object of interest moving, you should update the object's location.
* To keep track of the agent's belief on the object: If the agent and the object are in the same room, the agent can see the object, so the agent's belief will reflect the true location of the object. If the agent cannot see the object (the agent is in a different room or not in any rooms), the agent's belief will remain unchanged until the agent sees the object again.
3. Format your output exactly as shown in example answers below.

[EXAMPLE STORY1]
Step 0: Catherine is in the patio; Kristin is in the patio; the pencil sharpener is on the sauna's table; the thread spool is on the sauna's table.
Step 1: Catherine moves to the sauna.
Step 2: Catherine moves to the patio.
Step 3: Catherine moves to the sauna.
Step 4: Catherine moves the pencil sharpener to the sauna's nightstand.
Step 5: Catherine moves to the patio.
Step 6: Kristin moves to the sauna.
Step 7: Catherine moves to the sauna.
Step 8: Kristin leaves the room he was in.
Step 9: Catherine moves the thread spool to the sauna's nightstand.
Step 10: Kristin enters the patio.

[EXAMPLE QUESTION1]
Where does Catherine believe the thread spool is?

[EXAMPLE ANSWER1]
Catherine's belief on the thread spool:
- Step 0: (initial state) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: None}
- Step 1: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 2: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 3: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 4: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 5: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 6: (Catherine location unchanged; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 7: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 8: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 9: (Catherine location unchanged; thread spool location changed) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
- Step 10: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
Final Answer: the sauna's nightstand

[EXAMPLE STORY2]
Step 0: Kathryn is in the storage room; Mitchell is in the storage room; the rubber band is on the patio's coffee table; the fuse is on the patio's coffee table.
Step 1: Kathryn moves to the patio.
Step 2: Kathryn moves to the storage room, and moves the fuse to the storage room's ledge.
Step 3: Kathryn moves the fuse to the storage room's coffee table.
Step 4: Mitchell leaves the room he was in.
Step 5: Kathryn moves the fuse to the storage room's ledge.
Step 6: Mitchell enters the storage room.
Step 7: Kathryn moves to the patio, and moves the fuse to the patio's ledge.
Step 8: Kathryn moves the rubber band to the patio's ledge.
Step 9: Kathryn moves to the storage room, and moves the rubber band to the storage room's ledge.
Step 10: Mitchell moves the rubber band to the storage room's coffee table.

[EXAMPLE QUESTION2]
Where does Kathryn believe the fuse is?

[EXAMPLE ANSWER2]
Kathryn's belief on the fuse:
- Step 0: (initial state) {Kathryn location: storage room; fuse location: patio's coffee table; Kathryn sees fuse: False; Kathryn's belief on fuse: None}
- Step 1: (Kathryn location changed; fuse location unchanged) {Kathryn location: patio; fuse location: patio's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's coffee table}
- Step 2: (Kathryn location changed; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 3: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 4: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 5: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 6: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 7: (Kathryn location changed; fuse location changed) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 8: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 9: (Kathryn location changed; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
- Step 10: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
Final Answer: the patio's ledge

[PROBLEM]
Read the following story and answer the question. Please carefully follow the approach and examples provided above when solving the problem. Remember that the output format should follow the examples.

[STORY]
Step 0: Savannah is in the mudroom; Jose is in the balcony; the bookmark is on the mudroom's pedestal; the brush is on the balcony's pedestal.
Step 1: Savannah moves the bookmark to the mudroom's sideboard.
Step 2: Jose moves to the mudroom.
Step 3: Savannah moves to the balcony, and moves the bookmark to the balcony's pedestal.
Step 4: Savannah moves the brush to the balcony's sideboard.
Step 5: Savannah leaves the room he was in.
Step 6: Jose moves to the balcony.
Step 7: Savannah enters the balcony.
Step 8: Jose moves the brush to the balcony's pedestal.
Step 9: Savannah moves to the mudroom, and moves the brush to the mudroom's sideboard.
Step 10: Jose moves to the mudroom.
Step 11: Savannah moves to the balcony.
Step 12: Jose moves to the balcony.
Step 13: Savannah moves to the mudroom, and moves the bookmark to the mudroom's sideboard.
Step 14: Jose moves to the mudroom.
Step 15: Savannah moves to the balcony.
Step 16: Jose moves to the balcony.
Step 17: Savannah moves to the mudroom.
Step 18: Savannah moves to the balcony, and moves the brush to the balcony's pedestal.
Step 19: Savannah moves to the mudroom.
Step 20: Jose leaves the room he was in.
Step 21: Savannah moves the bookmark to the mudroom's pedestal.
Step 22: Jose enters the balcony.
Step 23: Savannah moves to the balcony.
Step 24: Jose leaves the room he was in.
Step 25: Savannah leaves the room he was in.
Step 26: Jose enters the mudroom.
Step 27: Savannah enters the mudroom.
Step 28: Jose leaves the room he was in.
Step 29: Savannah moves the bookmark to the mudroom's sideboard.
Step 30: Jose enters the mudroom.
Step 31: Savannah leaves the room he was in.
Step 32: Jose moves the bookmark to the mudroom's pedestal.
Step 33: Savannah enters the balcony.
Step 34: Jose leaves the room he was in.
Step 35: Savannah moves the brush to the balcony's sideboard.
Step 36: Jose enters the mudroom.
Step 37: Savannah moves to the mudroom.
Step 38: Jose moves the bookmark to the mudroom's sideboard.
Step 39: Savannah moves the bookmark to the mudroom's pedestal.
Step 40: Jose leaves the room he was in.

[QUESTION]
Where does Savannah believe the brush is?

[YOUR ANSWER]

Savannah's belief on the brush:
- Step 0: (initial state) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: None}
- Step 1: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: None}
- Step 2: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: None}
- Step 3: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 4: (Savannah location unchanged; brush location changed) {Savannah location: balcony; brush location: balcony's sideboard; Savannah sees brush: True; Savannah's belief on brush: balcony's sideboard}
- Step 5: (Savannah location changed; brush location unchanged) {Savannah location: None; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
- Step 6: (Savannah location unchanged; brush location unchanged) {Savannah location: None; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
- Step 7: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: balcony's sideboard; Savannah sees brush: True; Savannah's belief on brush: balcony's sideboard}
- Step 8: (Savannah location unchanged; brush location changed) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 9: (Savannah location changed; brush location changed) {Savannah location: mudroom; brush location: mudroom's sideboard; Savannah sees brush: True; Savannah's belief on brush: mudroom's sideboard}
- Step 10: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: mudroom's sideboard; Savannah sees brush: True; Savannah's belief on brush: mudroom's sideboard}
- Step 11: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: mudroom's sideboard; Savannah sees brush: False; Savannah's belief on brush: mudroom's sideboard}
- Step 12: (Savannah location unchanged; brush location unchanged) {Savannah location: balcony; brush location: mudroom's sideboard; Savannah sees brush: False; Savannah's belief on brush: mudroom's sideboard}
- Step 13: (Savannah location changed; brush location unchanged) {Savannah location: mudroom; brush location: mudroom's sideboard; Savannah sees brush: True; Savannah's belief on brush: mudroom's sideboard}
- Step 14: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: mudroom's sideboard; Savannah sees brush: True; Savannah's belief on brush: mudroom's sideboard}
- Step 15: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: mudroom's sideboard; Savannah sees brush: False; Savannah's belief on brush: mudroom's sideboard}
- Step 16: (Savannah location unchanged; brush location unchanged) {Savannah location: balcony; brush location: mudroom's sideboard; Savannah sees brush: False; Savannah's belief on brush: mudroom's sideboard}
- Step 17: (Savannah location changed; brush location unchanged) {Savannah location: mudroom; brush location: mudroom's sideboard; Savannah sees brush: True; Savannah's belief on brush: mudroom's sideboard}
- Step 18: (Savannah location changed; brush location changed) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 19: (Savannah location changed; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 20: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 21: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 22: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 23: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 24: (Savannah location unchanged; brush location unchanged) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 25: (Savannah location changed; brush location unchanged) {Savannah location: None; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 26: (Savannah location unchanged; brush location unchanged) {Savannah location: None; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 27: (Savannah location changed; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 28: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 29: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 30: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 31: (Savannah location changed; brush location unchanged) {Savannah location: None; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 32: (Savannah location unchanged; brush location unchanged) {Savannah location: None; brush location: balcony's pedestal; Savannah sees brush: False; Savannah's belief on brush: balcony's pedestal}
- Step 33: (Savannah location changed; brush location unchanged) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 34: (Savannah location unchanged; brush location unchanged) {Savannah location: balcony; brush location: balcony's pedestal; Savannah sees brush: True; Savannah's belief on brush: balcony's pedestal}
- Step 35: (Savannah location unchanged; brush location changed) {Savannah location: balcony; brush location: balcony's sideboard; Savannah sees brush: True; Savannah's belief on brush: balcony's sideboard}
- Step 36: (Savannah location unchanged; brush location unchanged) {Savannah location: balcony; brush location: balcony's sideboard; Savannah sees brush: True; Savannah's belief on brush: balcony's sideboard}
- Step 37: (Savannah location changed; brush location unchanged) {Savannah location: mudroom; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
- Step 38: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
- Step 39: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
- Step 40: (Savannah location unchanged; brush location unchanged) {Savannah location: mudroom; brush location: balcony's sideboard; Savannah sees brush: False; Savannah's belief on brush: balcony's sideboard}
Final Answer: the balcony's sideboard

Question: Where does Savannah believe the brush is?

Agents: [Savannah, Jose].
Objects: [the bookmark, the brush].
Rooms: [the balcony, the mudroom].
Containers: [the balcony's pedestal, the balcony's sideboard, the mudroom's pedestal, the mudroom's sideboard]


[TASK]
You'll see a story about object placement. Each story involves four components: Agents, Objects, Rooms, and Containers. Given a question about an (agent, object) pair, your task is to track the locations and beliefs in stories about object placement asked in the question.

[APPROACH]
You will solve the problem by tracking the location of the agent, location of the object, and the agent's belief of the object.
1. Initial Setup: set up agent's starting location, object's starting location, agent's initial belief on the object's location. Note that if an agent does not see an object at the start, their belief on the object is None.
2. Then, track step-by-step:
* If a step involves that the agent moves to another room, leaves a room, or enters a room, you should update the agent's location. Note that if the agent leaves the current room but hasn't entered another room, the agent's location is None.
* If a step involves the object of interest moving, you should update the object's location.
* To keep track of the agent's belief on the object: If the agent and the object are in the same room, the agent can see the object, so the agent's belief will reflect the true location of the object. If the agent cannot see the object (the agent is in a different room or not in any rooms), the agent's belief will remain unchanged until the agent sees the object again.
3. Format your output exactly as shown in example answers below.

[EXAMPLE STORY1]
Step 0: Catherine is in the patio; Kristin is in the patio; the pencil sharpener is on the sauna's table; the thread spool is on the sauna's table.
Step 1: Catherine moves to the sauna.
Step 2: Catherine moves to the patio.
Step 3: Catherine moves to the sauna.
Step 4: Catherine moves the pencil sharpener to the sauna's nightstand.
Step 5: Catherine moves to the patio.
Step 6: Kristin moves to the sauna.
Step 7: Catherine moves to the sauna.
Step 8: Kristin leaves the room he was in.
Step 9: Catherine moves the thread spool to the sauna's nightstand.
Step 10: Kristin enters the patio.

[EXAMPLE QUESTION1]
Where does Catherine believe the thread spool is?

[EXAMPLE ANSWER1]
Catherine's belief on the thread spool:
- Step 0: (initial state) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: None}
- Step 1: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 2: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 3: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 4: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 5: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 6: (Catherine location unchanged; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 7: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 8: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 9: (Catherine location unchanged; thread spool location changed) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
- Step 10: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
Final Answer: the sauna's nightstand

[EXAMPLE STORY2]
Step 0: Kathryn is in the storage room; Mitchell is in the storage room; the rubber band is on the patio's coffee table; the fuse is on the patio's coffee table.
Step 1: Kathryn moves to the patio.
Step 2: Kathryn moves to the storage room, and moves the fuse to the storage room's ledge.
Step 3: Kathryn moves the fuse to the storage room's coffee table.
Step 4: Mitchell leaves the room he was in.
Step 5: Kathryn moves the fuse to the storage room's ledge.
Step 6: Mitchell enters the storage room.
Step 7: Kathryn moves to the patio, and moves the fuse to the patio's ledge.
Step 8: Kathryn moves the rubber band to the patio's ledge.
Step 9: Kathryn moves to the storage room, and moves the rubber band to the storage room's ledge.
Step 10: Mitchell moves the rubber band to the storage room's coffee table.

[EXAMPLE QUESTION2]
Where does Kathryn believe the fuse is?

[EXAMPLE ANSWER2]
Kathryn's belief on the fuse:
- Step 0: (initial state) {Kathryn location: storage room; fuse location: patio's coffee table; Kathryn sees fuse: False; Kathryn's belief on fuse: None}
- Step 1: (Kathryn location changed; fuse location unchanged) {Kathryn location: patio; fuse location: patio's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's coffee table}
- Step 2: (Kathryn location changed; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 3: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 4: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 5: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 6: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 7: (Kathryn location changed; fuse location changed) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 8: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 9: (Kathryn location changed; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
- Step 10: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
Final Answer: the patio's ledge

[PROBLEM]
Read the following story and answer the question. Please carefully follow the approach and examples provided above when solving the problem. Remember that the output format should follow the examples.

[STORY]
Step 0: Wendy is in the laundry room; Catherine is in the laundry room; the business card is on the laundry room's mantel; the bottle cap is on the laundry room's desk.
Step 1: Wendy moves to the mudroom, and moves the business card to the mudroom's desk.
Step 2: Catherine moves to the mudroom, and moves the bottle cap to the mudroom's mantel.
Step 3: Wendy leaves the room he was in.
Step 4: Catherine moves to the laundry room, and moves the business card to the laundry room's mantel.
Step 5: Wendy enters the laundry room.
Step 6: Catherine moves the business card to the laundry room's desk.
Step 7: Wendy moves to the mudroom, and moves the business card to the mudroom's desk.
Step 8: Catherine moves to the mudroom.
Step 9: Wendy leaves the room he was in.
Step 10: Catherine moves the bottle cap to the mudroom's desk.
Step 11: Wendy enters the mudroom.
Step 12: Catherine moves to the laundry room, and moves the bottle cap to the laundry room's desk.
Step 13: Wendy moves to the laundry room.
Step 14: Catherine moves the bottle cap to the laundry room's mantel.
Step 15: Wendy moves the bottle cap to the laundry room's desk.
Step 16: Catherine moves to the mudroom.
Step 17: Wendy moves to the mudroom.
Step 18: Catherine moves the business card to the mudroom's mantel.
Step 19: Wendy leaves the room he was in.
Step 20: Catherine leaves the room he was in.
Step 21: Wendy enters the mudroom.
Step 22: Catherine enters the laundry room.
Step 23: Wendy moves to the laundry room.
Step 24: Catherine moves to the mudroom.
Step 25: Wendy moves to the mudroom.
Step 26: Catherine moves to the laundry room.
Step 27: Wendy moves the business card to the mudroom's desk.
Step 28: Catherine moves the bottle cap to the laundry room's mantel.
Step 29: Wendy leaves the room he was in.
Step 30: Catherine moves to the mudroom, and moves the bottle cap to the mudroom's desk.
Step 31: Wendy enters the mudroom.
Step 32: Catherine moves to the laundry room.
Step 33: Wendy moves to the laundry room, and moves the business card to the laundry room's mantel.
Step 34: Catherine moves to the mudroom.
Step 35: Wendy moves the business card to the laundry room's desk.
Step 36: Catherine leaves the room he was in.
Step 37: Wendy moves to the mudroom, and moves the business card to the mudroom's mantel.
Step 38: Catherine enters the laundry room.
Step 39: Wendy moves to the laundry room.
Step 40: Catherine moves to the mudroom.

[QUESTION]
Where does Wendy believe the bottle cap is?

[YOUR ANSWER]

Wendy's belief on the bottle cap:
- Step 0: (initial state) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 1: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 2: (Wendy location unchanged; bottle cap location changed) {Wendy location: mudroom; bottle cap location: mudroom's mantel; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's mantel}
- Step 3: (Wendy location changed; bottle cap location unchanged) {Wendy location: None; bottle cap location: mudroom's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 4: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: None; bottle cap location: mudroom's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 5: (Wendy location changed; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 6: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 7: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's mantel; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's mantel}
- Step 8: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's mantel; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's mantel}
- Step 9: (Wendy location changed; bottle cap location unchanged) {Wendy location: None; bottle cap location: mudroom's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 10: (Wendy location unchanged; bottle cap location changed) {Wendy location: None; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's mantel}
- Step 11: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's desk}
- Step 12: (Wendy location unchanged; bottle cap location changed) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 13: (Wendy location changed; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 14: (Wendy location unchanged; bottle cap location changed) {Wendy location: laundry room; bottle cap location: laundry room's mantel; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's mantel}
- Step 15: (Wendy location unchanged; bottle cap location changed) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 16: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 17: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 18: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 19: (Wendy location changed; bottle cap location unchanged) {Wendy location: None; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 20: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: None; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 21: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 22: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 23: (Wendy location changed; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 24: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: laundry room's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: laundry room's desk}
- Step 25: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 26: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 27: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: laundry room's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 28: (Wendy location unchanged; bottle cap location changed) {Wendy location: mudroom; bottle cap location: laundry room's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 29: (Wendy location changed; bottle cap location unchanged) {Wendy location: None; bottle cap location: laundry room's mantel; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 30: (Wendy location unchanged; bottle cap location changed) {Wendy location: None; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: laundry room's desk}
- Step 31: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's desk}
- Step 32: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's desk}
- Step 33: (Wendy location changed; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 34: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 35: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 36: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 37: (Wendy location changed; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's desk}
- Step 38: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: mudroom; bottle cap location: mudroom's desk; Wendy sees bottle cap: True; Wendy's belief on bottle cap: mudroom's desk}
- Step 39: (Wendy location changed; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
- Step 40: (Wendy location unchanged; bottle cap location unchanged) {Wendy location: laundry room; bottle cap location: mudroom's desk; Wendy sees bottle cap: False; Wendy's belief on bottle cap: mudroom's desk}
Final Answer: the mudroom's desk

Question: Where does Wendy believe the bottle cap is?

Agents: [Wendy, Catherine].
Objects: [the business card, the bottle cap].
Rooms: [the mudroom, the laundry room].
Containers: [the mudroom's desk, the mudroom's mantel, the laundry room's desk, the laundry room's mantel]


[TASK]
You'll see a story about object placement. Each story involves four components: Agents, Objects, Rooms, and Containers. Given a question about an (agent, object) pair, your task is to track the locations and beliefs in stories about object placement asked in the question.

[APPROACH]
You will solve the problem by tracking the location of the agent, location of the object, and the agent's belief of the object.
1. Initial Setup: set up agent's starting location, object's starting location, agent's initial belief on the object's location. Note that if an agent does not see an object at the start, their belief on the object is None.
2. Then, track step-by-step:
* If a step involves that the agent moves to another room, leaves a room, or enters a room, you should update the agent's location. Note that if the agent leaves the current room but hasn't entered another room, the agent's location is None.
* If a step involves the object of interest moving, you should update the object's location.
* To keep track of the agent's belief on the object: If the agent and the object are in the same room, the agent can see the object, so the agent's belief will reflect the true location of the object. If the agent cannot see the object (the agent is in a different room or not in any rooms), the agent's belief will remain unchanged until the agent sees the object again.
3. Format your output exactly as shown in example answers below.

[EXAMPLE STORY1]
Step 0: Catherine is in the patio; Kristin is in the patio; the pencil sharpener is on the sauna's table; the thread spool is on the sauna's table.
Step 1: Catherine moves to the sauna.
Step 2: Catherine moves to the patio.
Step 3: Catherine moves to the sauna.
Step 4: Catherine moves the pencil sharpener to the sauna's nightstand.
Step 5: Catherine moves to the patio.
Step 6: Kristin moves to the sauna.
Step 7: Catherine moves to the sauna.
Step 8: Kristin leaves the room he was in.
Step 9: Catherine moves the thread spool to the sauna's nightstand.
Step 10: Kristin enters the patio.

[EXAMPLE QUESTION1]
Where does Catherine believe the thread spool is?

[EXAMPLE ANSWER1]
Catherine's belief on the thread spool:
- Step 0: (initial state) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: None}
- Step 1: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 2: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 3: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 4: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 5: (Catherine location changed; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 6: (Catherine location unchanged; thread spool location unchanged) {Catherine location: patio; thread spool location: sauna's table; Catherine sees thread spool: False; Catherine's belief on thread spool: sauna's table}
- Step 7: (Catherine location changed; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 8: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's table; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's table}
- Step 9: (Catherine location unchanged; thread spool location changed) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
- Step 10: (Catherine location unchanged; thread spool location unchanged) {Catherine location: sauna; thread spool location: sauna's nightstand; Catherine sees thread spool: True; Catherine's belief on thread spool: sauna's nightstand}
Final Answer: the sauna's nightstand

[EXAMPLE STORY2]
Step 0: Kathryn is in the storage room; Mitchell is in the storage room; the rubber band is on the patio's coffee table; the fuse is on the patio's coffee table.
Step 1: Kathryn moves to the patio.
Step 2: Kathryn moves to the storage room, and moves the fuse to the storage room's ledge.
Step 3: Kathryn moves the fuse to the storage room's coffee table.
Step 4: Mitchell leaves the room he was in.
Step 5: Kathryn moves the fuse to the storage room's ledge.
Step 6: Mitchell enters the storage room.
Step 7: Kathryn moves to the patio, and moves the fuse to the patio's ledge.
Step 8: Kathryn moves the rubber band to the patio's ledge.
Step 9: Kathryn moves to the storage room, and moves the rubber band to the storage room's ledge.
Step 10: Mitchell moves the rubber band to the storage room's coffee table.

[EXAMPLE QUESTION2]
Where does Kathryn believe the fuse is?

[EXAMPLE ANSWER2]
Kathryn's belief on the fuse:
- Step 0: (initial state) {Kathryn location: storage room; fuse location: patio's coffee table; Kathryn sees fuse: False; Kathryn's belief on fuse: None}
- Step 1: (Kathryn location changed; fuse location unchanged) {Kathryn location: patio; fuse location: patio's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's coffee table}
- Step 2: (Kathryn location changed; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 3: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 4: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's coffee table; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's coffee table}
- Step 5: (Kathryn location unchanged; fuse location changed) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 6: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: storage room's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: storage room's ledge}
- Step 7: (Kathryn location changed; fuse location changed) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 8: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: patio; fuse location: patio's ledge; Kathryn sees fuse: True; Kathryn's belief on fuse: patio's ledge}
- Step 9: (Kathryn location changed; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
- Step 10: (Kathryn location unchanged; fuse location unchanged) {Kathryn location: storage room; fuse location: patio's ledge; Kathryn sees fuse: False; Kathryn's belief on fuse: patio's ledge}
Final Answer: the patio's ledge

[PROBLEM]
Read the following story and answer the question. Please carefully follow the approach and examples provided above when solving the problem. Remember that the output format should follow the examples.

[STORY]
Step 0: Paul is in the home theater; Tiffany is in the home theater; the brush is on the home theater's counter; the candle is on the home theater's bar.
Step 1: Paul moves to the patio, and moves the brush to the patio's bar.
Step 2: Tiffany leaves the room he was in.
Step 3: Paul moves the brush to the patio's counter.
Step 4: Tiffany enters the home theater.
Step 5: Paul moves the brush to the patio's bar.
Step 6: Tiffany moves to the patio.
Step 7: Paul moves to the home theater.
Step 8: Tiffany moves the brush to the patio's counter.
Step 9: Paul moves the candle to the home theater's counter.
Step 10: Tiffany moves to the home theater.
Step 11: Paul leaves the room he was in.
Step 12: Tiffany moves the candle to the home theater's bar.
Step 13: Paul enters the home theater.
Step 14: Tiffany moves to the patio, and moves the candle to the patio's counter.
Step 15: Tiffany moves the candle to the patio's bar.
Step 16: Tiffany moves to the home theater, and moves the candle to the home theater's counter.
Step 17: Paul moves to the patio, and moves the candle to the patio's bar.
Step 18: Tiffany moves to the patio.
Step 19: Paul moves the brush to the patio's bar.
Step 20: Tiffany moves to the home theater, and moves the brush to the home theater's bar.
Step 21: Paul moves to the home theater, and moves the candle to the home theater's bar.
Step 22: Tiffany moves the brush to the home theater's counter.
Step 23: Paul moves to the patio, and moves the candle to the patio's bar.
Step 24: Tiffany moves to the patio, and moves the brush to the patio's bar.
Step 25: Paul moves to the home theater.
Step 26: Tiffany moves to the home theater.
Step 27: Paul moves to the patio.
Step 28: Paul moves to the home theater, and moves the candle to the home theater's bar.
Step 29: Paul moves to the patio, and moves the candle to the patio's bar.
Step 30: Paul moves the brush to the patio's counter.
Step 31: Paul leaves the room he was in.
Step 32: Tiffany moves to the patio.
Step 33: Paul enters the home theater.
Step 34: Tiffany moves the brush to the patio's bar.
Step 35: Paul moves to the patio.
Step 36: Tiffany moves to the home theater, and moves the candle to the home theater's bar.
Step 37: Paul leaves the room he was in.
Step 38: Tiffany leaves the room he was in.
Step 39: Paul enters the home theater.
Step 40: Tiffany enters the home theater.

[QUESTION]
Where does Tiffany believe the brush is?

[YOUR ANSWER]

Tiffany's belief on the brush:
- Step 0: (initial state) {Tiffany location: home theater; brush location: home theater's counter; Tiffany sees brush: True; Tiffany's belief on brush: home theater's counter}
- Step 1: (Tiffany location unchanged; brush location changed) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: home theater's counter}
- Step 2: (Tiffany location changed; brush location unchanged) {Tiffany location: None; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: home theater's counter}
- Step 3: (Tiffany location unchanged; brush location changed) {Tiffany location: None; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: home theater's counter}
- Step 4: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: home theater's counter}
- Step 5: (Tiffany location unchanged; brush location changed) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: home theater's counter}
- Step 6: (Tiffany location changed; brush location unchanged) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 7: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 8: (Tiffany location unchanged; brush location changed) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 9: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 10: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 11: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 12: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 13: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 14: (Tiffany location changed; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 15: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 16: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 17: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's counter}
- Step 18: (Tiffany location changed; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 19: (Tiffany location unchanged; brush location changed) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 20: (Tiffany location changed; brush location changed) {Tiffany location: home theater; brush location: home theater's bar; Tiffany sees brush: True; Tiffany's belief on brush: home theater's bar}
- Step 21: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: home theater's bar; Tiffany sees brush: True; Tiffany's belief on brush: home theater's bar}
- Step 22: (Tiffany location unchanged; brush location changed) {Tiffany location: home theater; brush location: home theater's counter; Tiffany sees brush: True; Tiffany's belief on brush: home theater's counter}
- Step 23: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: home theater's counter; Tiffany sees brush: True; Tiffany's belief on brush: home theater's counter}
- Step 24: (Tiffany location changed; brush location changed) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 25: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 26: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 27: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 28: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 29: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 30: (Tiffany location unchanged; brush location changed) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 31: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's counter; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 32: (Tiffany location changed; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 33: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's counter; Tiffany sees brush: True; Tiffany's belief on brush: patio's counter}
- Step 34: (Tiffany location unchanged; brush location changed) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 35: (Tiffany location unchanged; brush location unchanged) {Tiffany location: patio; brush location: patio's bar; Tiffany sees brush: True; Tiffany's belief on brush: patio's bar}
- Step 36: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 37: (Tiffany location unchanged; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 38: (Tiffany location changed; brush location unchanged) {Tiffany location: None; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 39: (Tiffany location unchanged; brush location unchanged) {Tiffany location: None; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
- Step 40: (Tiffany location changed; brush location unchanged) {Tiffany location: home theater; brush location: patio's bar; Tiffany sees brush: False; Tiffany's belief on brush: patio's bar}
Final Answer: the patio's bar

Question: Where does Tiffany believe the brush is?

Agents: [Paul, Tiffany].
Objects: [the brush, the candle].
Rooms: [the home theater, the patio].
Containers: [the home theater's bar, the home theater's counter, the patio's bar, the patio's counter]