
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 dimensions $PQ=5$ and $QR=3$. A line $XY$ is constructed through $Q$ such that $XY$ is perpendicular to $PR$. Points $P$ and $S$ are located on $XQ$ and $YQ$, respectively. What is the length of $XY$?
A) $\frac{31\sqrt{34}}{15}$
B) $\frac{32\sqrt{34}}{12}$
C) $\frac{34\sqrt{34}}{15}$
D) $\frac{36\sqrt{34}}{15}$

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