
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 $\triangle XYZ$, $XY = 13, XZ = 12$, and $YZ = 5$. Circle $S$ is the circle with smallest radius which passes through $Z$ and is tangent to $XY$ at its midpoint. Determine the length of segment $WT$ where $W$ and $T$ are the points of intersection, distinct from $Z$, of circle $S$ with sides $XZ$ and $YZ$, respectively.
A) 12
B) 13
C) 14
D) 6.5
E) 13.5

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