
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 C1 has its center O lying on circle C2. The two circles meet at X and Y. Point Z in the exterior of C1 lies on circle C2 and XZ = 13, OZ = 11, and YZ = 7. Use the Pythagorean Theorem to determine the radius of circle C1.

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