
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 $f\left(x\right)=x^{3}-x^{2}+ax+b$, if the tangent line of the curve $y=f\left(x\right)$ at $\left(0,f\left(0\right)\right)$ is $y=-x+1$.  
$(1)$ Find the values of $a$ and $b$;  
$(2)$ Find the minimum value of the function $y=f\left(x\right)$ on $\left[-2,2\right]$.

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