
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 \(ABCD\) (\(AD \parallel BC\), \(AD > BC\)). A circle \(\Omega\) is inscribed in angle \(\angle BAD\), is tangent to segment \(BC\) at point \(C\), and intersects \(CD\) again at point \(E\) such that \(CE = 9\) and \(ED = 16\). Find the radius of the circle \(\Omega\) and the area of trapezoid \(ABCD\).

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