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

(I) Find the value of $m$.

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

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