
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
Consider two circles, one with a radius of 3 and another with a radius of 1, where the smaller circle is inside the larger one and tangent to it. A triangle $\triangle PQR$ has its vertices on the straight line tangents to both circles: side $\overline{PQ}$ is tangent to both the smaller circle and the larger circle, and sides $\overline{PR}$ and $\overline{QR}$ are congruent. Determine the total area of triangle $\triangle PQR$.

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