
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 a right triangle XYZ, where ∠XYZ = 90∘, the sides XY, XZ, and YZ are diameters of semicircles. The area of the semicircle on XY is 18π, and the arc of the semicircle on XZ has length 10π. Determine the radius of the semicircle on YZ.

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