
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 $f\left(x\right)=x^{2}-2ax+a$.  
$(1)$ If the solution set of $f\left(x\right)\geqslant 0$ is $R$, find the range of real number $a$;  
$(2)$ When $a\neq -3$, solve the inequality with respect to $x$: $f\left(x\right) \gt 4a-\left(a+3\right)x$.

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