
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 $26$ inches from the center. A secant from $P$ cuts the circle at $Q$ and $R$ so that the external segment of the secant $PQ$ is $15$ inches and $QR$ is $9$ inches. An additional tangent from $P$ touches the circle at point $S$. Find the radius of the circle.
A) $\sqrt{144}$ inches
B) $\sqrt{225}$ inches
C) $\sqrt{316}$ inches
D) $\sqrt{400}$ inches

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