
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) $$\frac {\sin(\pi+\alpha)\sin(2\pi-\alpha)\cos(-\pi-\alpha)}{\sin(3\pi +\alpha )\cos(\pi -\alpha )\cos( \frac {3\pi}{2}+\alpha )}$$
(2) $\cos20^\circ + \cos160^\circ + \sin1866^\circ - \sin(-606^\circ)$

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