
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 $l_1: ax+y-1=0$ and $l_2: x-y-3=0$, if the angle of inclination of line $l_1$ is $\frac{\pi}{4}$, then $a = \_\_\_\_\_\_$. If line $l_1$ is perpendicular to line $l_2$, then $a = \_\_\_\_\_\_$. If line $l_1$ is parallel to line $l_2$, then the distance between the two parallel lines is $\_\_\_\_\_\_$.

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