
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 a side length of 12 cm. At each of the four corners of the square, a quarter circle is drawn with each quarter circle having a 6 cm radius. Additionally, a complete circle with radius 3 cm is drawn centered at the square's center. Calculate the area of the shaded region which excludes the regions of the quarter circles and the central circle. Express your answer in terms of $\pi$.

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