
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
Two circles of radius 3 each are internally tangent to a smaller circle of radius 2 at points $A$ and $B$, where $AB$ is a diameter of the smaller circle. A square is inscribed in the smaller circle, with its sides parallel and perpendicular to $AB$. Calculate the area that is outside the smaller circle and inside each of the two larger circles, excluding the area covered by the square.

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