
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 sets $A=\{x|(x-2)[x-(3a+1)]<0\}$, $B=\left\{x\middle| \frac{x-2a}{x-(a^2+1)}<0\right\}$, where $a\neq 1$  
(1) When $a=2$, find $A\cap B$;  
(2) Find the range of real numbers $a$ for which $B\subseteq A$.

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