
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 = 2 * AC. Let D and E be on AB and BC, respectively, such that ∠BAE = ∠ACD. Let F be the intersection of segments AE and CD, and suppose that △CFE is equilateral. Find ∠ACB.

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