
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 $a$ and $b$ have the same sign, and the solution set of the quadratic inequality $ax^2+2x+b<0$ is $\{x|x\neq- \frac {1}{a}\}$, and $m=b+ \frac {1}{a}$, $n=a+ \frac {1}{b}$, calculate the maximum value of $m+n$.

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