
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 away from the center of a circle. A secant from $P$ intersects the circle at points $Q$ and $R$ such that the external segment $PQ$ is 10 inches long and segment $QR$ inside the circle is 8 inches long. Calculate the radius of the circle.
A) $10$ inches
B) $\sqrt{5}$ inches
C) $3\sqrt{5}$ inches
D) $5\sqrt{3}$ inches

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