
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 set $A=\left\{ x \mid y= \sqrt{\frac{x-4}{2-x}} \right\}$ and $B=\left\{ k \mid \text{the domain of } f(x)=\frac{x^2+x+1}{kx^2+kx+1} \text{ is } \mathbb{R} \right\}$.

1. Find the sets A and B.
2. If $f$ is a function from A to B such that $f: x \to y=\frac{2}{x-1}$, and if $a \in B$ but $a \notin \left\{ y \mid y=\frac{2}{x-1}, x \in A \right\}$, determine the range of values for the real number $a$.

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