
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 large circle has a diameter of 12 meters. Half of the circle is covered by a square that exactly fits over the half-circle. The side length of the square equals the radius of the circle. What is the total area that is not covered by the square in square meters? Express your answer in terms of \(\pi\).

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