
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 $f(x)=(m-1)^{2}x^{m^{2}-4m+2}$ is monotonically increasing on $(0, +\infty)$, and the function $g(x)=2^{x}-k$,
(Ⅰ) Find the value of $m$;
(Ⅱ) For $x \in [1,2]$, let the range of $f(x)$ and $g(x)$ be set $A$ and $B$ respectively. Let proposition $p$ be: $x \in A$, and proposition $q$ be: $x \in B$. If proposition $p$ is a necessary condition for proposition $q$ to hold, find the range of the real number $k$.

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