
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 $f\left( x \right)=ax^{3}+bx+c$ which attains an extreme value of $c-16$ at the point $x=2$,

(1) Find the values of $a$ and $b$;
(2) If $f\left( x \right)$ has a maximum value of $28$, find the minimum value of $f\left( x \right)$ on the interval $\left[ -3,3 \right]$.

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