
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 $l$ that does not pass through the second quadrant: $ax - y - 4 = 0$ and a circle: $x^2 + (y - 1)^2 = 5$. The line $l$ is tangent to the circle.

1. Find the equation of line $l$.
2. If line $l\_1$ passes through point $(3, -1)$ and is parallel to line $l$, and line $l\_2$ is symmetric to line $l\_1$ about the line $y = 1$, find the equation of line $l\_2$.

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