
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 quadratic function $f(x)=x^{2}+bx+c$, and $f(-3)=f(1)$, $f(0)=0$.  
(I) Find the explicit formula of the function $f(x)$;  
(II) If the function $g(x)=f(x)-(4+2a)x+2$, where $x\in[1,2]$, find the maximum and minimum values of the function $g(x)$.

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