
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 each other and exactly one side of $\triangle ABC$, respectively. The circles with centers $Q$ and $R$ are tangent to side $BC$, the circle with center $S$ is tangent to side $AC$ and the circle with center $P$ is tangent to side $AB$. If all circles are also mutually tangent to each other, find the length of side $BC$.

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