
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 quadratic function $f(x)=ax^{2}-2ax+b+1$ $(a > 0)$ has a maximum value of $4$ and a minimum value of $1$ in the interval $[2,3]$.
- (I) Find the expression of the function $f(x)$;
- (II) Let $g(x)= \frac{f(x)}{x}$. If the inequality $g(2^{x})-k\cdot2^{x}\geqslant 0$ holds for any $x\in[1,2]$, find the range of values for $k$.

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