
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
The vertices of a square are the centers of four circles. Each side of the square is 8cm and the radius of each circle is 3cm. Find the area, in square centimeters, of the shaded region created by the intersection of the square and the circles as previously described.

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