
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 function $f(x) = \log(3-x) + \sqrt{x-1}$ have a domain as the set A, and the function $g(x) = 2^x + a$ have a range as the set B.
(1) If $a=2$, find $A \cap B$ and $A \cup B$;
(2) If $A \cup B = B$, find the range of values for $a$.

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