
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 $XYZ$, point $P$ is on $\overline{XY}$ such that $XP:PY = 4:1$, and point $Q$ is on $\overline{YZ}$ such that $YQ:QZ = 4:1$. If lines $PQ$ and $XZ$ intersect at $R$, then find $\frac{PQ}{QR}$.

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