
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 two sets A and B, where $A=\{x \mid x^2-2x-3 \leq 0, x \in \mathbb{R}\}$ and $B=\{x \mid (x-m+2)(x-m-2) \leq 0, x \in \mathbb{R}, m \in \mathbb{R}\}$.  
(1) If $A \cap B = \{x \mid 0 \leq x \leq 3\}$, find the value of the real number $m$.  
(2) If $A \subseteq \overline{B}$ (where $\overline{B}$ denotes the complement of B in $\mathbb{R}$), find the range of values for the real number $m$.

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