
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
Stuart has drawn two concentric circles. He starts drawing chords $\overline{AB}$, $\overline{BC}, \ldots$ of the larger circle, each tangent to the smaller circle. If the interior angle $m\angle ABC = 60^\circ$, find how many segments Stuart will draw before returning to his starting point at $A$.

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