
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
Given Circle $C_1$ of radius $12$ units touches Circle $C_2$ externally at a point $P$, and a line through $P$ intersects $C_1$ at $Q$ and $C_2$ at $R$ such that $Q$ is closer to $P$ than $R$ is, with $PQ=7$ units and $PR=17$ units, calculate the radius of $C_2$.

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