
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 circle centered on the diagonal \( AC \) of the trapezoid \( ABCD \) (\( BC \parallel AD \)) passes through vertices \( A \) and \( B \), touches side \( CD \) at point \( C \), and intersects the base \( AD \) at point \( E \). Find the area of trapezoid \( ABCD \) if \( CD = 6 \sqrt{13} \) and \( AE = 8 \).

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