
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]


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Through the vertices of an equilateral triangle \(ABC\), parallel lines \(AD\), \(BE\), and \(CF\) are drawn. The line \(BE\) lies between the lines \(AD\) and \(CF\) and divides the distance between them in the ratio \(m:n\), starting from the line \(AD\). Find the angle \(BCF\).

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