
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 three concentric circles with radii $r_1 < r_2 < r_3$. He draws chords $\overline{AB}$, $\overline{BC}, \ldots$ of the largest circle ($r_3$), each tangent to the middle circle ($r_2$) and the smallest circle ($r_1$). If $m\angle ABC=60^\circ$, how many segments will Stuart draw before returning to his starting point at $A$?

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