
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
Determine the domains of the functions $f(x) = \sqrt{\frac{x+1}{x-2}}$ and $g(x) = \frac{1}{\sqrt{x^2 - (2a+1)x + a^2 + a}}$, denoted as set A and set B, respectively. 
(1) Find sets A and B.
(2) If $A \cup B = B$, find the range of values for the real number $a$.

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