
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 that line $l_{1}$ passes through points $A(m,1)$ and $B(-3,4)$, and line $l_{2}$ passes through points $C(1,m)$ and $D(-1,m+1)$, for what value of $m$ do the lines $l_{1}$ and $l_{2}$

$(1)$ intersect at a right angle;

$(2)$ are parallel;

$(3)$ the angle of inclination of $l_{1}$ is $45^{\circ}$

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