
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 three lines $l_1$: $4x+y-4=0$, $l_2$: $mx+y=0$, $l_3$: $x-my-4=0$ that do not intersect at the same point:

(1) When these three lines cannot form a triangle, find the value of the real number $m$.

(2) When $l_3$ is perpendicular to both $l_1$ and $l_2$, find the distance between the two foot points.

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