
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
ABCD is a rhombus. Points \( E \) and \( F \) lie on sides \( AB \) and \( BC \), respectively, such that \( \frac{AE}{BE} = \frac{BF}{CF} = 5 \). The triangle \( DEF \) is equilateral. Find the angles of the rhombus.

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