
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 points A (1, 2) and B (5, -1),
(1) If the distance from points A and B to line $l$ is both 2, find the equation of line $l$;
(2) If the distance from points A and B to line $l$ is both $m$ ($m>0$), discuss the number of possible lines $l$ based on the value of $m$. There is no need to write out the equation of the line.

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