
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 trapezoid $PQRS$ with $\overline{QR}\parallel\overline{PS}$, let $QR = 1500$ and $PS = 2800$. Let $\angle P = 45^\circ$, $\angle S = 45^\circ$, and $T$ and $U$ be the midpoints of $\overline{QR}$ and $\overline{PS}$, respectively. Find the length $TU$.

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