
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 sets $A=\{x|x^{2}+2x-3=0,x\in R\}$ and $B=\{x|x^{2}-\left(a+1\right)x+a=0,x\in R\}$.<br/>$(1)$ When $a=2$, find $A\cap C_{R}B$;<br/>$(2)$ If $A\cup B=A$, find the set of real numbers for $a$.

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