
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
Rectangle $PQRS$ has $PQ = 5$ and $QR = 12$. Point $T$ is the foot of the perpendicular from $Q$ to diagonal $\overline{PS}$, and point $U$ is the foot of the perpendicular from $R$ to diagonal $\overline{PS}$. Find the area of $\triangle PTS$ and $\triangle PSU$.
A) 15
B) 20
C) 30
D) 35
E) 40

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