
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
$PQRS$ is a rectangular sheet of paper that has been folded so that corner $Q$ is matched with point $Q'$ on edge $PS.$ The crease is $LM,$ where $L$ is on $PQ$ and $M$ is on $RS.$ The dimensions $PL=5, QL=13,$ and $MS=4$ are given. The perimeter of rectangle $PQRS$ is $x/y,$ where $x$ and $y$ are relatively prime positive integers. Find $x+y.$

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