
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 $ABC$ (not drawn to scale). The triangle $ABC$ is isosceles with $AB = AC$ and $\angle BAC = 120^\circ$. The circles are tangent to sides $AB$, $BC$, and $AC$ respectively. Find the perimeter of triangle $ABC$.

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