
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 $f\left(x\right)=x^{3}+2ax^{2}+bx+a-1$ attains an extremum of $0$ at $x=-1$, where $a$ and $b$ are real numbers. <br/>$(Ⅰ)$ Find the values of $a$ and $b$; <br/>$(Ⅱ)$ When $x\in \left[-1,1\right]$, find the maximum value of $f\left(x\right)$.

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