
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 located 15 inches from the center of a circle. A secant drawn from \( P \) intersects the circle at points \( Q \) and \( R \) such that the external segment \( PQ \) measures 10 inches and the internal segment \( QR \) measures 8 inches. Determine the radius of the circle.
A) \( 3\sqrt{5} \) inches
B) \( 4\sqrt{5} \) inches
C) \( 5\sqrt{5} \) inches
D) \( 6\sqrt{5} \) inches

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