
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 the lines $l_1: ax+2y-1=0$ and $l_2: x+by-3=0$, where the angle of inclination of $l_1$ is $\frac{\pi}{4}$, find the value of $a$. If $l_1$ is perpendicular to $l_2$, find the value of $b$. If $l_1$ is parallel to $l_2$, find the distance between the two lines.

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