
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 $f\left(x\right)=4x^{2}-4ax+a^{2}-2a+2$.  
$(1)$ If $a=2$, find the maximum and minimum values of the function $f\left(x\right)$ on the interval $\left[-1,3\right)$.  
$(2)$ If the function $f\left(x\right)$ has a minimum value of $3$ on the interval $\left[0,2\right]$, find the value of $a$.

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