
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 quadrilateral $ABCD$, sides $AB = 14$, $BC = 16$, $CD = 14$, $DA = 16$, and diagonals $AC$ and $BD$ intersect at right angles at point $O$, dividing them into equal halves. Point $P$ is on side $AB$ such that $OP$ is perpendicular to $AB$. If $X$ is the midpoint of $AD$ and $Y$ is the midpoint of $BC$, compute the ratio of the area of trapezoid $ABYX$ to the area of trapezoid $XYCD$.

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