
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 $f(x)= \frac {1}{3}x^{3}-ax^{2}+3x+b$ where $a,b \in \mathbb{R}$.  
(I) When $a=2$, $b=0$, find the range of $f(x)$ on $[0,3]$.  
(II) For any $b$, if the function $g(x)=|f(x)|- \frac {2}{3}$ has no more than $4$ zeros, find the range of $a$.

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