
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) $\dfrac{\cos(\alpha - \frac{\pi}{2})}{\sin(\frac{5}{2}\pi + \alpha)} \cdot \sin(\alpha - \pi) \cdot \cos(2\pi - \alpha)$;

(2) $\dfrac{\sqrt{1 - 2\sin 20^\circ \cos 200^\circ}}{\cos 160^\circ - \sqrt{1 - \cos^2 20^\circ}}$.

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