
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
Let the domain of the function $$f(x)= \sqrt {1-2^{x}}$$ be the set A, and the domain of the function $$g(x)=\log[(x-a+1)(x-a-1)]$$ be the set B.  
(I) Find the set A;  
(II) If $A \cap B = A$, find the range of the real number $a$.

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