
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 $l_1: 2x+y+2=0$, $l_2: mx+4y+n=0$  
(1) If $l_1 \perp l_2$, find the value of $m$;  
(2) If $l_1 \parallel l_2$, and their distance is $\sqrt{5}$, find the values of $m$ and $n$.

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