
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
Evaluate the sum $$\frac 1{\sin 30^\circ\sin 31^\circ} + \frac 1{\sin 32^\circ\sin 33^\circ} + \cdots + \frac 1{\sin 118^\circ\sin 119^\circ}$$ and determine a value for $m$ such that this sum equals $\frac{1}{\sin m^\circ}$.

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