
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 the diagram, four circles of radius 2 with centers $P$, $Q$, $R$, and $S$ are tangent to one another and to the sides of $\triangle ABC$. The centers form a configuration where $PQ$, $PR$, $PS$, $RQ$, and $RS$ are line segments connecting each pair of circle centers. Each side of $\triangle ABC$ is tangent to two circles, and each circle is tangent to two sides of the triangle and another circle. Find the perimeter of $\triangle ABC$.

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