
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 $XYZ$ has vertices $X(0,10)$, $Y(3,0)$, and $Z(10,0)$. A vertical line intersects $XZ$ at point $U$ and line segment $\overline{YZ}$ at point $V$, forming triangle $UVZ$. If the area of $\triangle UVZ$ is 20, find the positive difference of the $x$ and $y$ coordinates of point $U$.

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