
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
In triangle $PQR$, $N$ is the midpoint of $\overline{QR}$, $PQ = 15$, and $PR = 20$. Let $X$ be on $\overline{PR}$, and $Y$ be on $\overline{PQ}$, and let $Z$ be the intersection of $\overline{XY}$ and $\overline{PN}$. If $PX = 3PY$, then find $\frac{XZ}{ZY}$.

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