
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
Circles \(P\), \(Q\), and \(R\) are externally tangent to each other and internally tangent to circle \(S\). Circles \(Q\) and \(R\) are congruent. Circle \(P\) has radius 2 and passes through the center of \(S\). What is the radius of circle \(Q\)?

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