
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 convex \( n \)-gon \( P \), where \( n > 3 \), is divided into equal triangles by diagonals that do not intersect inside it.

What are the possible values of \( n \) if the \( n \)-gon is inscribed?

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