
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 circle of radius 2 is internally tangent to two circles of radius 3 at points $A$ and $B$, where $AB$ is a diameter of the smaller circle. Calculate the area of the region that is outside the smaller circle and inside each of the two larger circles. Express your answer in terms of $\pi$ and in simplest radical form.

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