
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
Given that in the right triangle PQR, PQ=15, QR=8, and angle R is a right angle, a semicircle is inscribed in the triangle, touching PQ and QR at their midpoints and the hypotenuse PR. Additionally, a smaller semicircle is inscribed such that it is tangent to the larger semicircle and also touches sides PQ and QR, determine the radius of the smaller semicircle.

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