
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
Given the side lengths of triangle $XYZ$ are $XY=20$, $YZ=28$, and $XZ=32$, and points $P$ and $Q$ are on $XY$ and $XZ$ respectively, with $XP=8$ and $XQ=5$, determine the ratio of the area of triangle $XPQ$ to the area of quadrilateral $PQZY$.

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