
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 placed on \( AB \) and \( BC \), respectively, such that \( \angle BAE = \angle ACD \). Suppose \( F \), the intersection point of \( AE \) and \( CD \), creates an equilateral triangle \( CFE \). Determine \( \angle ACB \).
**A)** \( 45^\circ \)  
**B)** \( 60^\circ \)  
**C)** \( 75^\circ \)  
**D)** \( 90^\circ \)  
**E)** \( 120^\circ \)

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