
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
(1) Let $U=\mathbb{R}$, and the sets $A=\{x|x^2+3x+2=0\}$, $B=\{x|x^2+(m+1)x+m=0\}$. If $(\complement_U A) \cap B = \emptyset$, find the value of $m$.  
(2) Let the sets $A=\{x|-2\leq x \leq 5\}$, $B=\{x|n+1\leq x \leq 2n-1\}$, and $B \subseteq A$. Find the range of values for $n$.

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