
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 equilateral $\triangle ABC$, as shown. The circle centers $P$, $Q$, $R$, and $S$ are positioned such that lines through $P, Q$ and $R, S$ are parallel to $AB$, lines through $P, R$ and $Q, S$ are parallel to $BC$, and $P, S$ and $Q, R$ are positioned along line segments parallel to $AC$. 

Find the perimeter of triangle $ABC$.

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