
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 with centers $P$, $Q$, $R$, and $S$ each have a radius of 2. These circles are tangent to one another and to the sides of $\triangle ABC$ as shown. The circles centered at $P$ and $Q$ are tangent to side $AB$, the circle at $R$ is tangent to side $BC$, and the circle at $S$ is tangent to side $AC$. Determine the perimeter of $\triangle ABC$ if $\triangle ABC$ is isosceles with $AB = AC$.

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