
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: x + my + 6 = 0 $ and $ l_2: (m-2)x + 3y + 2m = 0 $, if $ l_1 \parallel l_2 $, then the distance between $ l_1 $ and $ l_2 $ is __________.

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