
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
$$ \frac{1}{\sin 15^\circ \sin 16^\circ} + \frac{1}{\sin 17^\circ \sin 18^\circ} + \cdots + \frac{1}{\sin 173^\circ \sin 174^\circ} = \frac{1}{\sin n^\circ}. $$

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