
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 \(ABCD\) (\(AD \parallel BC\)) and a rectangle \(A_1B_1C_1D_1\) are inscribed in a circle \(\Omega\) with a radius of 10 in such a way that \(AC \parallel B_1D_1\) and \(BD \parallel A_1C_1\). Find the ratio of the areas of \(ABCD\) and \(A_1B_1C_1D_1\) given that \(AD = 16\) and \(BC = 12\).

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