
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
Triangle $ABC$ has $AB = AC$. Let $D$ and $E$ be points on $\overline{AB}$ and $\overline{AC}$ respectively, such that $AD = DE = EC$. Let $F$ be the intersection of segments $BD$ and $CE$, and suppose that $\triangle BDF$ is equilateral. What is $\angle BAC$?
A) $30^\circ$
B) $45^\circ$
C) $60^\circ$
D) $75^\circ$
E) $90^\circ$

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