
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 its vertices at the centers of four circles. A fifth circle is placed inside the square, touching all four circles. Given that the side of the square is 8cm and the radius of each of the four outer circles is 3cm, find the area of the shaded region, defined as the interior of the square but outside all the circles.

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