
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 universal set $U=\mathbb{R}$, $A=\{x\in\mathbb{R}|x^2-3x+b=0\}$, $B=\{x\in\mathbb{R}|(x-2)(x^2+3x-4=0)\}$.  
(1) If $b=4$, there exists a set $M$ such that $A$ is a proper subset of $M$, and $M$ is a proper subset of $B$. Find all such sets $M$.  
(2) Can the sets $A$ and $B$ satisfy $(\complement_{U}B) \cap A = \emptyset$? If so, find the range of the real number $b$; if not, explain why.

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