
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 $l_{1}$: $x+3y+18=0$ and $l_{2}$: $2x+3y-8=0$, point $A$ is taken on line $l_{1}$ and point $B$ is taken on line $l_{2}$. A line $l_{3}$ parallel to line $l_{2}$ is drawn passing through the midpoint of segment $AB$. <br/>$(1)$ Find the distance between lines $l_{1}$ and $l_{2}$; <br/>$(2)$ Find the equation of line $l_{3}$.

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