
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
Christina draws a pair of concentric circles. She draws chords $\overline{DE}$, $\overline{EF}, \ldots$ of the larger circle, each chord being tangent to the smaller circle. If $m\angle DEF = 85^\circ$, how many segments will she draw before returning to her starting point at $D$?

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