
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 with side length \(4\) has the same center as a circle with radius \(2\sqrt{2}\). Calculate the area of the region shared by both the square and the circle.
A) \(4\pi\)  
B) \(8\pi\)  
C) \(12\pi\)  
D) \(16\pi\)

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