
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 $PQRS$, leg $\overline{QR}$ is perpendicular to bases $\overline{PQ}$ and $\overline{RS}$, and diagonals $\overline{PS}$ and $\overline{QR}$ are perpendicular. Given that $PQ=5$ and $PS=10\sqrt{10}$, find $QR^2$.

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