
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 $l_1$: $ax - by + 4 = 0$, $l_2$: $(a-1)x + y + b = 0$, find the values of $a$ and $b$ that satisfy the following conditions:  
$(1)$ Line $l_1$ passes through the point $(-3,-1)$, and line $l_1$ is perpendicular to line $l_2$;  
$(2)$ Line $l_1$ is parallel to line $l_2$, and the distance from the origin to $l_1$ and $l_2$ is equal.

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