
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
In the following complex polygon, each side is perpendicular to its adjacent sides, and all 32 of its sides are congruent. The total perimeter of this polygon is 64 units. Find the area of the polygon.

(Imagine a somewhat similar setup to the previous drawing but adjusted for more sides and possibly a more extended perimeter layout, still maintaining all sides as congruent.)

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