
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 convex quadrilateral $PQRS$ side $\overline{RS}$ is perpendicular to diagonal $\overline{PQ}$, side $\overline{PQ}$ is perpendicular to diagonal $\overline{RS}$, $RS = 72$, and $PQ = 30$. The line through $Q$ perpendicular to side $\overline{PS}$ intersects diagonal $\overline{PR}$ at $T$ with $PT = 40$. Find $TR$.

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