
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 function $g(x)=x^{2}+(m+2)x+m-2$, defined for $x\in (-\infty, 0]$, determine the interval $[a,b]$ such that $\left[\frac{k}{b},\frac{k}{a}\right]=[\frac{2}{m+2},\frac{2}{m}]\left(\frac{1}{8}\right)$.

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