
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 $f(x)=- \frac {1}{3}x^{3}+ \frac {a}{2}x^{2}-2x$ $(a\in\mathbb{R})$.  
$(1)$ When $a=3$, find the intervals of monotonicity for the function $f(x)$.  
$(2)$ If for any $x\in[1,+\infty)$, $f′(x) < 2(a-1)$ holds, find the range of the real number $a$.  
$(3)$ If through the point $(0,- \frac {1}{3})$ three different tangents can be drawn to the graph of the function $y=f(x)$, find the range of the real number $a$.

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