
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
A right triangle $XYZ$ has side lengths $YZ = 9$, $XZ = 12$, and $XY = 15$. A circle centered at $Q$ is tangent to line $YZ$ at $Y$ and passes through $X$. A circle centered at $R$ is tangent to line $XZ$ at $X$ and passes through $Y$. What is the distance $QR$?
A) 10
B) 12.5
C) 15
D) 17.5
E) 20

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