
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 $l\_1$: $x+my+1=0$ and $l\_2$: $(m-3)x-2y+(13-7m)=0$.
(1) If $l\_1 \perp l\_2$, find the value of the real number $m$;
(2) If $l\_1 \parallel l\_2$, find the distance $d$ between $l\_1$ and $l\_2$.

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