
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
In a diagram, six circles of radius 2 with centers $P$, $Q$, $R$, $S$, $T$, and $U$ are tangent to one another and to the sides of $\triangle ABC$. The circles are positioned such that $P$, $Q$, and $R$ are tangent to side $AB$, $S$ is tangent to side $BC$, and both $T$ and $U$ are tangent to side $CA$. Determine the perimeter of $\triangle ABC$.

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