
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 that the side lengths of triangle XYZ are XY = 30, YZ = 45, and XZ = 54, and points P and Q are on XY and XZ respectively, with XP = 18 and XQ = 27, find the ratio of the area of triangle XPQ to the area of the quadrilateral PQYZ.

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