
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 a regular 20-sided polygon, four consecutive vertices \( A, B, C, \) and \( D \) are marked. A point \( E \) is chosen inside the polygon such that \( A E = D E \) and \( \angle B E C = 2 \angle C E D \). Find the angle \( \angle A E B \).

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