
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 that $m$ is a real number, and the function $f(x)= \frac {2m}{3}x^{3}+x^{2}-3x-mx+2$, $g(x)=f′(x)$, where $f′(x)$ is the derivative of $f(x)$.  
$(1)$ When $m=1$, find the intervals of monotonicity for $f(x)$;  
$(2)$ If $g(x)$ has a zero in the interval $[-1,1]$, find the range of values for $m$.

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