
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 $f\left(x\right)=x^{2}+\left(2-a\right)x-2a$, where $a\in R$.  
$(1)$ If the graph of $f\left(x\right)$ is symmetric about the line $x=1$, find the range of the function $f\left(x\right)$ on the interval $\left[0,4\right]$;  
$(2)$ Find the range of values for the independent variable $x$ for which $f\left(x\right) \gt 0$.

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