
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 $f(x) = \frac{1}{3}x^3 - \frac{1}{2}x^2 + 2x$, and $g(x) = \frac{1}{2}ax^2 - (a-2)x$,

(I) For any real number $x \in [-1, 2]$, the derivative of $f(x)$ is always less than or equal to $m$. Find the minimum value of $m$.

(II) If the equation $f(x) = g(x)$ has three distinct real roots in the interval $(-1, +\infty)$, find the range of values for $a$.

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