
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 a triangle $PQR$, where $P=(0,8)$, $Q=(0,0)$, and $R=(10,0)$, point $S$ is the midpoint of $\overline{PQ}$, and point $T$ is the midpoint of $\overline{QR}$. Determine the sum of the $x$ and $y$ coordinates of $U$, the point of intersection of $\overline{PT}$ and $\overline{RS}$.

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