
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 $XYZ$ with $\angle XYZ = 90^\circ$, three quarter circles are drawn with diameters along the sides of the triangle. The area of the quarter circle on $\overline{XY}$ is $2\pi$ and the arc length of the quarter circle on $\overline{XZ}$ is $6\pi$. Calculate the radius of the quarter circle on $\overline{YZ}$.
A) 12.00
B) 12.33
C) 13.00
D) 14.00
E) 12.50

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