
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 a square diagram, four circles of radius 2 with centers at $P$, $Q$, $R$, and $S$ are arranged such that each circle is tangent to two adjacent sides of the square and each adjacent pair of circles is tangent to each other. Find the side length of the square.

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