
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 two parallel lines \\(l_{1}\\): \\(\sqrt{3}x-y+1=0\\) and \\(l_{2}\\): \\(\sqrt{3}x-y+3=0\\).
\\((1)\\) If line \\(n\\) is perpendicular to both \\(l_{1}\\) and \\(l_{2}\\), and the area of the triangle formed with the coordinate axes is \\(2\sqrt{3}\\), find the equation of line \\(n\\).
\\((2)\\) If line \\(m\\) passes through the point \\((\sqrt{3},4)\\) and the segment cut off by \\(l_{1}\\) and \\(l_{2}\\) has a length of \\(2\\), find the equation of line \\(m\\).

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