
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
An octagon is inscribed in a square so that each vertex of the octagon bisects the sides of the square. The perimeter of the square is 80 centimeters. Calculate the area of the inscribed octagon in square centimeters.

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