
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 a circle, an isosceles triangle $\triangle ABC$ (where $AB = AC$) is inscribed with $\angle BAC = 80^{\circ}$. Points $D$, $E$, and $F$ are the midpoints of arcs $BC$, $CA$, and $AB$ (not containing the opposite vertex, respectively). Determine the measure of $\angle DEF$.

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