
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 circle $C_1$ has its center $O$ on a line $\ell$. Two points $P$ and $Q$ on $\ell$ are tangents to $C_1$, with $O$ between $P$ and $Q$. The distances are $OP = 9$, and $OQ = 15$. If another point $R$ exists on $C_1$ such that $\angle PRQ = 90^\circ$, what is the radius of $C_1$?
A) 10
B) 12
C) $\sqrt{153}$
D) $\sqrt{168}$

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