
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 \( \triangle PQR \) has side-lengths \( PQ = 15, QR = 30, \) and \( PR = 20. \) The line through the incenter of \( \triangle PQR \) parallel to \( \overline{QR} \) intersects \( \overline{PQ} \) at \( X \) and \( \overline{PR} \) at \( Y. \) What is the perimeter of \( \triangle PXY? \)

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