
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 $ABC$, $AB = 3 \cdot AC$. Points $D$ and $E$ are on segments $\overline{AB}$ and $\overline{BC}$, respectively, such that $\angle BAE = \angle ACD$. Let $G$ be the intersection of $AE$ and $CD$. Suppose that triangle $BEG$ is equilateral. Determine the measure of $\angle ACB$.
A) $60^\circ$
B) $75^\circ$
C) $90^\circ$
D) $105^\circ$
E) $120^\circ$

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