
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
Let $A=\{x|x^{2}-3x+2=0\}$, $B=\{x|x^{2}+2(a+1)x+(a^{2}-5)=0\}$.  
$(1)$ If $A\cap B=\{2\}$, find the value of the real number $a$;  
$(2)$ If $U=R$, $A\cap (\complement _{U}B)=A$. Find the range of values for the real number $a$.

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