
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 decagon is inscribed in a square so that each square side is quartered by the vertices of the decagon. The perimeter of the square is 160 centimeters. Calculate the area of the decagon inscribed in the square.

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