
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 $l_{1}$: $ax - by + 4 = 0$ and $l_{2}$: $(a - 1)x + y + b = 0$, find the values of $a$ and $b$ that satisfy the following conditions:
1. $l_{1} \perp l_{2}$ and $l_{1}$ passes through point $M(-3, -1)$;
2. $l_{1} \parallel l_{2}$ and the distance from the origin $O(0, 0)$ to $l_{1}$ and $l_{2}$ is equal.

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