
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 regular hexagon is inscribed in a square so that each side of the square is bisected by the vertices of the hexagon. If the perimeter of the square is 160 centimeters, what is the area of the hexagon?

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