
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 power function $f(x) = (m-1)^2x^{m^2-4m+2}$ is monotonically increasing on $(0, +\infty)$, and the function $g(x) = 2^x - k$.
(Ⅰ) Find the value of $m$;
(Ⅱ) When $x \in [1, 2]$, let the range of $f(x)$ and $g(x)$ be set $A$ and $B$ respectively. If $A \cup B = A$, find the range of the real number $k$.

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