
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 rectangle such that the vertices of the octagon trisect the longer sides of the rectangle and bisect the shorter sides. The perimeter of the rectangle is 200 centimeters, and the ratio of the length to the width of the rectangle is 2:1. What is the area of the octagon?

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