
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 $f\left(x\right)=x^{2}-ax-a+3$, where $a\in R$.  
$(1)$ When $a=2$, if $x\in \left[0,3\right]$, find the range of $f\left(x\right)$;  
$(2)$ If $f\left(x\right)$ has two zeros, denoted as $x_{1}$ and $x_{2}$, and $x_{1}x_{2} \gt 0$, find the range of values for $a$.

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