
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 \( ABC \), \( AB = AC \) and the angle \( \angle BAC = 20^\circ \). Let \( E \) and \( F \) be points on the sides \( AB \) and \( AC \) such that \( \angle BCE = 50^\circ \) and \( \angle CBF = 60^\circ \). What is the angle between the lines \( BC \) and \( EF \)?

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