
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 trapezium \(ABCD\), the lines \(AB\) and \(DC\) are parallel, \(BC = AD\), \(DC = 2 \times AD\), and \(AB = 3 \times AD\). The angle bisectors of \(\angle DAB\) and \(\angle CBA\) intersect at the point \(E\). What fraction of the area of the trapezium \(ABCD\) is the area of the triangle \(ABE\)?

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