
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 $l_1: mx+8y+n=0$ and $l_2: 2x+my-1=0$,  
(1) If $l_1$ and $l_2$ intersect at point $P(m, -1)$, find the values of $m$ and $n$;  
(2) If $l_1 \parallel l_2$, determine the conditions that $m$ and $n$ must satisfy;  
(3) If $l_1 \perp l_2$, determine the conditions that $m$ and $n$ must satisfy.

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