
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 $A=\{x|x^2-3x-4\leq0\}$, $B=\{x|x^2-2mx+m^2-9\leq0\}$, $C=\{y|y=2^x+b, x\in\mathbb{R}\}$  
(1) If $A\cap B=[0,4]$, find the value of the real number $m$;  
(2) If $A\cap C=\emptyset$, find the range of the real number $b$;  
(3) If $A\cup B=B$, find the range of the real number $m$.

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