
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 $f(x) = \frac{1}{3}x^3 - ax^2 + 3x + b$ ($a, b \in \mathbb{R}$).  
(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 values for $a$.

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