
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 octagon is inscribed in a square so that each vertex of the octagon divides one side of the square into segments with lengths in the ratio 1:2:1. If the perimeter of the square is 216 centimeters, what is the number of square centimeters in the area of the octagon?

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