
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 $A=\{x\,|\,x^2-2x-3\leq0\}$ and $B=\{x\,|\,m-2\leq x \leq m+2\}$.

(1) If $A\cup B=A$, find the range of real numbers m.
(2) If $A\cap B=\{x\,|\,0\leq x \leq 3\}$, find the value of the real number m.

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