
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 $PQR$ has vertices $P(0,10)$, $Q(3,0)$, and $R(10,0)$. A vertical line intersects $PR$ at $T$ and $\overline{QR}$ at $U$, forming triangle $TUR$. If the area of $\triangle TUR$ is 15, determine the positive difference of the $x$ and $y$ coordinates of point $T$.

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