
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
Let \(ABC\) be an equilateral triangle. Let \(\overrightarrow{AB}\) be extended to a point \(D\) such that \(B\) is the midpoint of \(\overline{AD}\). A variable point \(E\) is taken on the same plane such that \(DE = AB\). If the distance between \(C\) and \(E\) is as large as possible, what is \(\angle BED\)?

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