
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 rectangle \(ABCD\) is given. A point \(E\) is placed on side \(BC\) so that one of the triangles \(ABE\), \(AED\), or \(CED\) is isosceles. It is known that the angle \(\angle AED\) is 80 degrees. Find the measure of the angle \(\angle BEA\). In your answer, list all possible values in ascending order, separated by commas or semicolons.

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