
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
Start with an angle of \(60^\circ\) and bisect it, then bisect the lower \(30^\circ\) angle, then the upper \(15^\circ\) angle, and so on, always alternating between the upper and lower of the previous two angles constructed. This process approaches a limiting line that divides the original \(60^\circ\) angle into two angles. Find the measure (degrees) of the smaller angle.

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