
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 $f(x)= \frac {1}{3}x^{3}-ax^{2}+bx(a,b\in R)$, with $f′(0)=f′(2)=1$.  
$(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $(3,f(3))$;  
$(2)$ If the function $g(x)=f(x)-4x$, for $x\in[-3,2]$, find the intervals of monotonicity and the minimum value of $g(x)$.

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