
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 square has sides of length 8, and a circle is inscribed such that it is tangent to two of the square's sides and centered along the square's perimeter. What is the area of the union of the regions enclosed by the square and the circle? Express your answer in terms of $\pi$.

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