
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

On the sides $AB, BC,$ and $CA$ of an equilateral triangle $ABC$, points $D, E,$ and $F$ are chosen respectively such that $DE \parallel AC$ and $DF \parallel BC$. Find the angle between the lines $AE$ and $BF$.

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