
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 $f(x)=-x^{3}+3ax^{2}-4$ ($a\in\mathbb{R}$).  
$(1)$ If $a\neq 0$, find the intervals of monotonicity for $f(x)$;  
$(2)$ If the function $f(x)$ attains an extremum of $- \dfrac {7}{2}$ at $x=b$, and $g(x)=f(x)+mx$ is monotonically decreasing on $[0,2]$, find the range of the real number $m$.

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