
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a room, there are several stools (3 legs each) and chairs (4 legs each), and each stool or chair can only seat one person. Some people came in for a meeting, and there were not enough stools or chairs for everyone if they only chose one type, but everyone had a seat, and there were still empty seats. It is known that when all the stools and chairs are occupied, the total number of legs (including people's, stools', and chairs') is 32. Determine the total number of people, stools, and chairs in the room.

Present the answer in LaTex format: \boxed{Your answer}
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