
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 the solution set of the inequality $\frac{x+2}{x+1} < 0$ is $\{x|a < x < b\}$, and the point $A(a,b)$ lies on the line $mx+ny+1=0$, where $mn > 0$, then the minimum value of $\frac{2}{m}+\frac{1}{n}$ is ______.

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