
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 $m$ passes through the point $(\sqrt{3}, 4)$ and the segment intercepted by $l_1$ and $l_2$ has a length of 2, find the equation of line $m$.

(2) 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 $n$.

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