
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
Find the least positive integer $n$ such that:
$$\frac 1{\sin 30^\circ\sin 31^\circ}+\frac 1{\sin 32^\circ\sin 33^\circ}+\cdots+\frac 1{\sin 89^\circ\sin 90^\circ}=\frac 1{\sin n^\circ}.$$

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