
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
The curve $y = 2\sin x$ cuts the line whose equation is $y = 2\sin 80^\circ$ into segments having the successive ratios 
\[\dots p : q : p : q \dots\] with $p < q.$ Compute the ordered pair of relatively prime positive integers $(p,q).$

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