
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 isosceles triangle \(ABC\) with equal sides \(AB\) and \(CB\), the sides \(AB\) and \(CB\) are extended beyond point \(B\) to points \(D\) and \(E\) respectively. The segments \(AE\), \(ED\), and \(DC\) are equal to each other, and \(\angle BED \neq \angle BDE\). Find the angle \(ABE\).

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