
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
The floor plan of an exhibition hall is a concave $n$-gon. We need to place guards in the hall such that each point of every wall is visible from the position of some guard. What is the maximum number of guards needed?

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