
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, three circles, each with radius 2, with centers $P$, $Q$, and $R$, are tangent to each other and tangent to the sides of $\triangle ABC$. Circle $P$ is tangent to side $AB$, circle $Q$ to $AC$, and circle $R$ to $BC$. The centers form $\triangle PQR$ inside $\triangle ABC$. Determine the perimeter of $\triangle ABC$ given the internal triangle $PQR$ is equilateral.

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