
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 $f(x)=ax^{3}+bx+c$ has an extremum at $x=2$ with the value $c-16$.  
(I) Find the values of $a$ and $b$;  
(II) If $f(x)$ has a maximum value of $28$, find the minimum value of $f(x)$ on the interval $[-3,3]$.

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