
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 the following expressions:

\\((1) \dfrac{\sin (\pi+\alpha)\sin (2\pi-\alpha)\cos (-\pi-\alpha)}{\sin (3\pi+\alpha)\cos (\pi-\alpha)\cos ( \dfrac{3\pi}{2}+\alpha)} \\)

\\((2)\cos 20^{\circ}+\cos 160^{\circ}+\sin 1866^{\circ}-\sin (606^{\circ})\\)

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