
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
Let \(\triangle ABC\) be equilateral, and let \(D, E, F\) be points on sides \(BC, CA, AB\) respectively, with \(FA = 9\), \(AE = EC = 6\), and \(CD = 4\). Determine the measure (in degrees) of \(\angle DEF\).

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