
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 $O$ on circle $C_2$. They intersect at points $X$ and $Y$. Point $Z$ outside $C_1$ lies on $C_2$ with $XZ=17$, $OZ=15$, and $YZ=9$. Find the radius of circle $C_1$.
A) $7\sqrt{12}$  
B) $8\sqrt{13}$  
C) $6\sqrt{14}$  
D) $9\sqrt{11}$

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