
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 triangle $ABC$, $AB=AC$. Point $D$ is on $\overline{AC}$ such that $\overline{BD}$ bisects angle $ABC$. Point $E$ is on $\overline{AB}$ such that $\overline{CE}$ bisects angle $ACB$. If $BD=BC$ and $CE=CB$, find the measure, in degrees, of angle $A$.

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