
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 $A = \{x | x^2 - 2x - 3 \leq 0, x \in \mathbb{R}\}$, $B = \{x | x^2 - 2mx + m^2 - 4 \leq 0, x \in \mathbb{R}, m \in \mathbb{R}\}$.

(1) If $A \cap B = [0,3]$, find the value of the real number $m$;

(2) If $A \subseteq \complement_{\mathbb{R}} B$, find the range of the real number $m$.

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