
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 $l_{1}: ax-by+4=0$ and $l_{2}: (a-1)x+y+b=0$. Find the values of $a$ and $b$ that satisfy the following conditions:  
(1) The line $l_{1}$ passes through the point $(-3,-1)$, and line $l_{1}$ is perpendicular to $l_{2}$.  
(2) The line $l_{1}$ is parallel to the line $l_{2}$, and the distances from the origin to $l_{1}$ and $l_{2}$ are equal.

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