
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
Let \( n \geq 3 \) be an integer. What is the largest possible number of interior angles greater than \( 180^\circ \) in an \( n \)-gon in the plane, given that the \( n \)-gon does not intersect itself and all its sides have the same length?

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