
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
Convex quadrilateral $PQRS$ has $PQ = 15$ and $RS = 20$. Diagonals $PR$ and $QS$ intersect at $T$, $PR = 22$, and $\triangle PTR$ and $\triangle QTS$ have equal areas. What is $PT$?
A) 8
B) 9
C) 10
D) 11
E) 12

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