
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 trapezoid $ABCD$, sides $AB$ and $CD$ are parallel with $AB = 15$ and $CD = 25$. The diagonals $AC$ and $BD$ intersect at point $O$, and the lines $AD$ and $BC$ are not parallel. Points $X$ and $Y$ are the midpoints of sides $AD$ and $BC$, respectively. A line through $X$ and $Y$ divides the trapezoid into two smaller trapezoids $ABYX$ and $XYCD$. Point $P$ is on $AB$ such that $OP$ is perpendicular to $AB$. Find the ratio of the area of trapezoid $ABYX$ to the area of trapezoid $XYCD$ in simplified form and the sum of the ratio's terms.

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