
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
A trapezoid $ABCD$ and a rectangle $A_{1}B_{1}C_{1}D_{1}$ are inscribed in a circle $\Omega$ with radius 13, such that $AD \parallel BC$, $AC \perp B_{1}D_{1}$, and $BD \perp A_{1}C_{1}$. Find the ratio of the area of $ABCD$ to the area of $A_{1}B_{1}C_{1}D_{1}$, given that $AD = 10$ and $BC = 24$.

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