
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 function $y=f(x)$ with its derivative $f′(x)$ in the interval $D$. The derivative of $f′(x)$ is denoted as $g(x)$. If $g(x) < 0$ holds true throughout the interval $D$, then the function $y=f(x)$ is considered to be "strictly concave" in the interval $D$. Given $f(x)=\frac{1}{12}{{x}^{4}}-\frac{m}{6}{{x}^{3}}-\frac{3}{2}{{x}^{2}}$ (where $m∈R$).

(I) Find the range of values for the real number $m$ if $y=f(x)$ is a "strictly concave function" in the interval $[0,3]$;

(II) If $f(x)$ is a "strictly concave function" in the interval $(a,b)$ for any real number $m$ that satisfies $|m|≤slant 2$, find the maximum value of $b-a$.

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