
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
From vertex  $A$  of an equilateral triangle  $ABC$ , a ray  $Ax$  intersects  $BC$  at point  $D$ . Let  $E$  be a point on  $Ax$  such that  $BA =BE$ . Calculate  $\angle AEC$ .

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