
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 $l_1$: $(m+3)x+4y=5-3m$ and $l_2$: $2x+(m+5)y=8$. For what values of $m$ do the following conditions hold: (1) $l_1$ is parallel to $l_2$; (2) $l_1$ coincides with $l_2$; (3) $l_1$ is perpendicular to $l_2$.

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