
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
Circle $C_1$ has its center $O$ lying on circle $C_2$. The two circles meet at points $X$ and $Y$. Point $Z$ in the exterior of $C_1$ lies on circle $C_2$, and $XZ = 15$, $OZ = 17$, and $YZ = 8$. What is the radius of circle $C_1$?

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