
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 \( ABC \), \( AC = 2 \cdot AB \). Points \( D \) and \( E \) are placed on line segments \( \overline{AB} \) and \( \overline{BC} \), respectively, such that \( \angle BAE = \angle ACD \). If point \( F \) is the intersection of segments \( AE \) and \( CD \), and triangle \( BFE \) is equilateral, determine the measure of \( \angle BAC \).

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