
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
The function $f(x) = \sqrt{\frac{3-x}{x}}$ is defined on the domain $A$; the function $g(x) = \log_2 (x-m)(x-m+2)$ is defined on the domain $B$.  
(1) When $m=1$, find $A \cap \complement_{\mathbb{R}} B$;  
(2) If $A \subseteq B$, find the range of the real number $m$.

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