
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 $A=\{x|x^{2}+3x+2=0\}$, $B=\{x|x^{2}+\left(m+1\right)x+m=0\}$.  
$(1)$ Express the set $A$ using the enumeration method.  
$(2)$ If $x\in B$ is a necessary condition for $x\in A$, find the value of the real number $m$.

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