
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 are externally tangent at point T. Lines $\overline{PAB}$ and $\overline{PA'B'}$ are common tangents to the circles, with points $A$ and $A'$ on the smaller circle, and $B$ and $B'$ on the larger circle. If $PA = AB = 6$, and the radius of the larger circle is three times the radius of the smaller circle, find the area of the smaller circle.

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