
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 $A=\{x\,|\,|x-1|<2\}$, $B=\{x\,|\,x^2-2mx+m^2-1<0\}$.  
(1) When $m=3$, find $A\cap B$;  
(2) If $A\cup B=A$, find the range of the real number $m$.

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