
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 $A=\{x|-1<x<2\}$, and $B=\{0,1,2\}$.
(1) Find $A\cap B$, $A\cup B$;
(2) Let the domain of the function $f(x)=\log_{3}(x-1)$ be set $C$, find $(\mathbb{R}\setminus C) \cap A$;
(3) Let set $M=\{x|a<x\leq a+2\}$, and $M\subseteq A$, find the range of the real number $a$.

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