
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 $l\_1$: $(m-2)x+3y+2m=0$, $l\_2$: $x+my+6=0$
(1) If line $l\_1$ is perpendicular to line $l\_2$, find the value of the real number $m$;
(2) If line $l\_1$ is parallel to line $l\_2$, find the value of the real number $m$.

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