
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 lines $l\_1$: $(m+2)x+(m+3)y-5=0$ and $l\_2$: $6x+(2m-1)y-5=0$, find the real values of $m$ for which:
1. $l\_1$ and $l\_2$ intersect?
2. $l\_1$ is parallel to $l\_2$?
3. $l\_1$ and $l\_2$ coincide?

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