
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)\\) calculate \\( \dfrac{\sqrt{3}\sin(\alpha-\pi)+5\cos(2\pi-\alpha)}{-\sqrt{3}\cos(\dfrac{3\pi}{2}+\alpha)+\cos(\pi+\alpha)}\\).

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