
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 bisected by the vertex of the octagon. The perimeter of the square is 160 centimeters. Calculate the area of the octagon and find the radius of the circle that can be inscribed within this octagon.

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