
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
$$
\frac{1}{\sin 30^\circ \sin 31^\circ} + \frac{1}{\sin 32^\circ \sin 33^\circ} + \cdots + \frac{1}{\sin 148^\circ \sin 149^\circ} = \frac{1}{\sin n^\circ}.
$$

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