
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 $\overline{AB}$ and $\overline{BC}$, respectively, such that $\angle BAE = \angle ACD$ and $\angle BAE = 2 \times \angle BCA$. Let $F$ be the intersection of segments $AE$ and $CD$. Suppose that $\triangle CFE$ is isosceles with $CF = FE$. What is $\angle ACB$?
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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