
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
Two circles with radii 4 and 3 touch each other externally. Common external tangents \(PQ\) and \(RS\) are drawn to these circles such that points \(P\) and \(S\) belong to the circle with the larger radius, and points \(Q\) and \(R\) belong to the circle with the smaller radius. Find the radius of the circle that is tangent to the segments \(RS\), \(SP\), and \(PQ\).

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