
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
Determine the ordered pair of relatively prime positive integers (p, q) such that the curve \( y = \sin x \) intersects the horizontal line \( y = \sin 60^\circ \) in a pattern that divides the x-axis into segments with successive ratios \( \dots p : q : p : q \dots \).

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