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

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