
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
Simplify: 

(1) \(\frac{1}{\sin 45^{\circ} \sin 46^{\circ}} + \frac{1}{\sin 47^{\circ} \sin 48^{\circ}} + \cdots + \frac{1}{\sin 133^{\circ} \sin 134^{\circ}}\)

(2) \(\frac{1}{\sin 1^{\circ} \sin 2^{\circ}} + \frac{1}{\sin 2^{\circ} \sin 3^{\circ}} + \cdots + \frac{1}{\sin 89^{\circ} \sin 90^{\circ}}\)

(3) \(2 \sin 2^{\circ} + 4 \sin 4^{\circ} + 6 \sin 6^{\circ} + \cdots + 180 \sin 180^{\circ}\)

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