
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 $A = \{x \mid y = \sqrt{\frac{x-4}{2-x}}\}$, and set $B = \{k \mid f(x) = \frac{x^2+x+1}{kx^2+kx+1}\}$ where the domain of $f(x)$ is $\mathbb{R}$.
(I) Assuming $f$ is a function from $A$ to $B$ defined by $f:x \to y = \frac{2}{x-1}$, and given that $a \in B$ but $a \notin \{y \mid y = f(x), x \in A\}$, find the range of real numbers for $a$.
(II) If proposition $p$: "$m \in A$" and proposition $q$: "$m \in B$", given that "p and q" is false, but "p or q" is true, find the range for the real number $m$.

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