
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 line $l\_1$ passing through point $A(-2,m)$ and point $B(m,4)$, line $l\_2$ as $2x+y-1=0$, and line $l\_3$ as $x+ny+1=0$. If $l\_1$ is parallel to $l\_2$ and $l\_2$ is perpendicular to $l\_3$, find the value of $m+n$.

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