
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 $f\left(x\right)=x^{3}+ax^{2}+bx-1\left(a,b\in R\right)$ has a local extremum of $4$ at $x=-1$.<br/>$(1)$ Find the values of $a$ and $b$;<br/>$(2)$ Find the extreme values of the function $y=f\left(x\right)$ on the interval $\left[0,4\right]$.

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