
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
Two triangles, $\triangle PQR$ and $\triangle PXY$, share a common vertex $P$ and angle $P$. The lengths of $PQ$ and $PR$ are 5 and 7 units, respectively. If the side $PX$ is three times the length of $PQ$, and $\angle PQR = \angle PXY$, find the length of the side $PY$ that makes the area of $\triangle PXY$ equal to three times the area of $\triangle PQR$.
A) 6 units
B) 7 units
C) 8 units
D) 10 units

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