
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
Given that the terminal side of angle $\alpha$ lies on the line $y=-\sqrt{3}x$,
(1) Find $\tan\alpha$, and write the set $S$ of angles that have the same terminal side as $\alpha$;
(2) Evaluate $\frac{\sqrt{3}\sin(\alpha-\pi)+5\cos(2\pi-\alpha)}{-\sqrt{3}\cos(\frac{3\pi}{2}+\alpha)+\cos(\pi+\alpha)}$.

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