
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
In $\triangle XYZ$, $XY = 13, XZ = 5$, and $YZ = 12$. Circle $S$ is the circle with the smallest radius which passes through $Z$ and is tangent to $XY$. Let $U$ and $V$ be the points of intersection, distinct from $Z$, of circle $S$ with sides $XZ$ and $YZ$, respectively. Calculate the length of segment $UV$.
**A)** $\frac{120}{13}$  
**B)** $\frac{60}{13}$  
**C)** $\frac{240}{13}$  
**D)** $\frac{30}{13}$

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