
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 function $f(x)=\sqrt{\frac{x-1}{x+1}}$ with domain $A$, and the function $g(x)=\log[(x-a)(x-1)]$ with domain $B$, where $a < 1$.

(1) Find the sets $A$ and $B$;

(2) If $B \subseteq A$, find the range of values for the real number $a$.

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