
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 $l_{1}:ax-by-1=0$ and $l_{2}:(a+2)x+y+a=0$, where $a$ and $b$ are non-zero constants.

(1) If $b=0$ and $l_{1}\bot l_{2}$, find the value of the real number $a$.

(2) If $b=2$ and $l_{1}\parallel l_{2}$, find the distance between the lines $l_{1}$ and $l_{2}$.

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