
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 $l\_1$: $(m+3)x+2y=5-3m$ and $l\_2$: $4x+(5+m)y=16$, find the values of $m$ that satisfy the following conditions:

(1) $l\_1$ and $l\_2$ intersect;

(2) $l\_1$ and $l\_2$ are parallel;

(3) $l\_1$ and $l\_2$ coincide (overlap);

(4) $l\_1$ and $l\_2$ are perpendicular.

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