
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 such that each side of the square is trisected by the vertices of the octagon. The perimeter of the square is now 144 centimeters. What is the area of the octagon inscribed in the square?

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