
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
$\triangle XYZ \sim \triangle WUT$, where $YZ = 15\text{ cm}$. Find the length of $UT$ if $WT = 10\text{ cm}$ and $WU = 12\text{ cm}$. [asy]
draw((0,0)--(15,0)--(15,9)--cycle);
draw((10,0)--(10,7.2));
label("$Y$",(0,0),SW);
label("$T$",(10,0),S);
label("$W$",(10,7.2),NW);
label("$X$",(15,9),NE);
label("$Z$",(15,0),SE);
label("10",(5,0),S);
label("12",(15,4.5),E);
[/asy]

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