
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 $XYZ$, side lengths are $XY = 30$, $YZ = 45$, and $XZ = 51$. Points P and Q are on $XY$ and $XZ$ respectively, such that $XP = 18$ and $XQ = 15$. Determine the ratio of the area of triangle $XPQ$ to the area of quadrilateral $PQZY$.
A) $\frac{459}{625}$
B) $\frac{1}{2}$
C) $\frac{3}{5}$
D) $\frac{459}{675}$

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