
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
A rectangle $PQRS$ has sides $PQ = 5$ and $QR = 12$. Point $T$ is the foot of the perpendicular from $Q$ to the diagonal $\overline{PS}$. Determine the area of $\triangle PTS$.
A) $\frac{140}{13}$
B) $\frac{150}{13}$
C) $\frac{160}{13}$
D) $\frac{170}{13}$

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