
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 right triangle $XYZ$, shown below, $\cos{Z} = \frac{12\sqrt{221}}{221}$. Find $XZ$.
[asy]
draw((0,0)--(9,0)--(0,12)--cycle,black+linewidth(1));
draw(rightanglemark((9,0),(0,0),(0,12),20),black+linewidth(1));
label("$X$",(0,0),W);
label("$Y$",(9,0),E);
label("$Z$",(0,12),N);
label("$\sqrt{221}$",(9,0)--(0,12),NE);
[/asy]

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