
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 a line $l: ax-y-4=0$ that does not pass through the second quadrant and is tangent to the circle $x^2+(y-1)^2=5$.
(1) Find the equation of line $l$;
(2) If line $l_1$ passes through the point $(3, -1)$ and is parallel to line $l$, and line $l_2$ is symmetric to line $l_1$ with respect to the line $y=1$, find the equation of line $l_2$.

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