
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 that set $A$ is the domain of the function $f(x)=\log_{\frac{1}{2}}(x-1)$, and set $B$ is the range of the function $g(x)=2^x$, where $x \in [-1, 2]$.  
(1) Find the set $A$;  
(2) Find the set $B$.

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