
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 $l\_1$: $ax + by + 1 = 0$, ($(a, b)$ is not simultaneously $0$), and $l\_2$: $(a - 2)x + y + a = 0$,
(1) If $b = 0$ and $l\_1 \perp l\_2$, find the value of the real number $a$;
(2) When $b = 3$ and $l\_1 \parallel l\_2$, find the distance between lines $l\_1$ and $l\_2$.

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