
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 two lines $l_{1}$: $x+(1+m)y=2-m$ and $l_{2}$: $2mx+4y=-16$, for what value(s) of $m$ are $l_{1}$ and $l_{2}$:  
$(1)$ intersecting;      
$(2)$ parallel;      
$(3)$ perpendicular.

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