
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 each at points $P$ and $Q$, where $PQ$ is a diameter of the smaller circle. The centers of the larger circles are shifted such that one is at $(0, -2)$ and the other at $(0, 2)$. Find the area of the region outside the smaller circle and inside each of the two larger circles. Express your solution in terms of $\pi$ and in simplest radical form.

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