
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 hexadecagon (16-sided polygon) is inscribed in a square such that the vertices of the hexadecagon quadrisection the sides of the square. The perimeter of the square is 160 centimeters. What is the area of the inscribed hexadecagon?

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