
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 \(ABC\), \(\angle A = 50^\circ\), \(\angle B = 60^\circ\), and \(\angle C = 70^\circ\). A ray of light bounces from point \(D\) on \(BC\) to \(E\) on \(CA\) to \(F\) on \(AB\) and then back to \(D\). Find the angles of \(\triangle DEF\).

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