
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 point P(2, 2) is on the curve $y=ax^3+bx$, if the slope of the tangent line at point P is 9, then:  
(i) $ab= \boxed{-3}$;  
(ii) The range of the function $f(x)=ax^3+bx$, where $x\in\left[-\frac{3}{2}, 3\right]$, is $\boxed{[-2, 18]}$.

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