
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 right triangle $PQR$, $PQ=15$, $QR=8$, and angle $R$ is a right angle. A semicircle is inscribed in the triangle such that it touches $PQ$ and $QR$ at their midpoints and the hypotenuse $PR$. What is the radius of the semicircle?
A) $\frac{24}{5}$

B) $\frac{12}{5}$

C) $\frac{17}{4}$

D) $\frac{15}{3}$

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