
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
Triangle $PQR$ has side-lengths $PQ = 15, QR = 30,$ and $PR = 22.$ The line through the incenter of $\triangle PQR$ parallel to $\overline{PR}$ intersects $\overline{PQ}$ at $X$ and $\overline{QR}$ at $Y.$ What is the perimeter of $\triangle PXY?$

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