
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 lines $l\_1$: $x+my+6=0$ and $l\_2$: $(m-2)x+3my+2m=0$.
(1) For what value of $m$ are $l\_1$ and $l\_2$ parallel;
(2) For what value of $m$ are $l\_1$ and $l\_2$ perpendicular.

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