
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 $f(x)={{\left( m-1 \right)}^{2}}{{x}^{{{m}^{2}}-4m+2}}$ is monotonically increasing on $(0,+\infty)$, and the function $g(x)=2^{x}-k$.

(I) Find the value of $m$;

(II) When $x\in[1,2]$, let the range of $f(x)$ and $g(x)$ be set $A$ and $B$ respectively. If proposition $p$: $x\in A$ is a necessary condition for proposition $q$: $x\in B$ to hold, find the range of the real number $k$.

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