
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 an isosceles trapezoid \( A B C D \) (\(A D \parallel B C\), \(A D > B C\)). A circle \( \Omega \) is inscribed in the angle \( B A D \), touches the segment \( B C \) at point \( C \), and intersects \( C D \) again at point \( E \), such that \( C E = 16 \) and \( E D = 9 \). Find the radius of the circle \( \Omega \) and the area of the trapezoid \( A B C D \).

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