
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 domain of the function $f(x)= \sqrt{-x^{2} + (a+2)x - a - 1}$ (where $a > 0$) is set A, and the range of the function $g(x) = 2^x - 1$ (for $x \leq 2$) is set B.
(1) When $a=1$, find the sets A and B;
(2) If sets A and B satisfy $A \cup B = B$, find the range of the real number $a$.

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