
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 the area of the semicircle along $\overline{PQ}$ is $50\pi$, and the circumference of the semicircle along $\overline{PR}$ is $18\pi$, find the radius of the semicircle that uses $\overline{QR}$ as its diameter, as well as the measure of the angle formed by the radii from the center to point $Q$ in the semicircle on $\overline{PR}$.

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