
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
Let the function $f(x)= \frac {1}{3}x^{3}- \frac {1}{2}x^{2}+2x$, $g(x)= \frac {1}{2}ax^{2}-(a-2)x$,  
$(I)$ For any real number $x\in[-1,2]$, $f′(x)\leqslant m$ always holds, find the minimum value of $m$;  
$(II)$ If the equation $f(x)=g(x)$ has three different 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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