
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 solution set for the inequality $x^2 + ax + b \leq 0$ is $A = [m, n]$, and the solution set for the inequality $$\frac{(x + 2)(x + 1)}{x - 1} > 0$$ is $B$, if $A \cup B = (-2, +\infty)$ and $A \cap B = (1, 3]$, find the value of $m + n$.

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