
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 point $P$ is outside a circle and is $15$ inches from the center. A secant drawn from $P$ cuts the circle at points $Q$ and $R$ such that the external segment $PQ$ measures $10$ inches and the internal segment $QR$ measures $8$ inches. Find the radius of the circle.
A) 5 inches
B) 4.5 inches
C) $3\sqrt{5}$ inches
D) $\sqrt{45}$ inches
E) 6 inches

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