
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
Let $k$ be a real number. The solution set $A$ of the system of inequalities about $x$ $\left\{\begin{array}{c}{x}^{2}+kx+1>0\\ k{x}^{2}+x+2<0\end{array}\right.$ is denoted as $A$. If $2 \notin A$, then the range of values for $k$ is ______.

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