
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
In the right trapezoid \(ABCD\) (with \(BC\) parallel to \(AD\) and \(AB\) perpendicular to \(AD\)), the shorter base \(AD\) is equal to 3, and the leg \(CD\) is equal to 6. Point \(E\), the midpoint of side \(CD\), is connected by a line segment to point \(B\).

It is known that the angle \(CBE\) is \(\alpha\). Find the area of trapezoid \(ABCD\).

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