
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 that the line $l\_1$ passes through points $A(-2, m)$ and $B(m, 4)$, the line $l\_2$ is defined by the equation $2x + y - 1 = 0$, and the line $l\_3$ is defined by the equation $x + ny + 1 = 0$. If $l\_1$ is parallel to $l\_2$ and $l\_2$ is perpendicular to $l\_3$, find the value of the real number $m + n$.

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