
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
A pair of vertices of a simple polygon is said to be "visible" to each other if and only if they are adjacent or the line segment connecting them lies entirely inside the polygon (excluding the endpoints on the boundary). Given a simple polygon with \( n \) vertices, where each vertex is exactly visible to four other vertices, find all possible values of the positive integer \( n \).

Note: A simple polygon is a polygon without holes and does not intersect itself.

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