
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 a triangle with  $\angle A=60^o, AB\ne AC$  and let  $AD$  be the angle bisector of  $\angle A$ . Line  $(e)$  that is perpendicular on the angle bisector  $AD$  at point  $A$ , intersects the extension of side  $BC$  at point  $E$  and also  $BE=AB+AC$ . Find the angles  $\angle B$  and  $\angle C$  of the triangle  $ABC$ .

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