
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 $ABC$, angle $ABC$ is $60^\circ$ and $\overline{AD}$ still bisects angle $BAC$. Additionally, $\overline{EC}$ is an external bisector of angle $BCA$, making angle $ECA$ twice the measure of angle $ACB$. Find the measurement of angle $AEC$.
A) $30^\circ$
B) $45^\circ$
C) $60^\circ$
D) $75^\circ$
E) $90^\circ$

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