
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
Trapezoid $PQRS$ has bases $PQ = 15$ units and $RS = 36$ units. Diagonals $PR$ and $QS$ intersect at point $T$. The area of trapezoid $PQRS$ is $387$ square units. If the diagonals divide each other in a ratio of 3:5, what is the area of triangle $QTS$?

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