
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 decagon is inscribed in a square so that each side of the square is divided into five equal segments, with vertices of the decagon at each division point. The perimeter of the square is 200 centimeters. What is the area of the decagon?

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