
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 sets $$A=\{x|y=lg(x-1)- \sqrt {x+2}\}$$ and $$B=\{x|x^{2}-3x+a=0\}$$.
(1) Find $A \cap B$ when $a=2$.
(2) Find the range of values for $a$ when $A \cup B = A$.

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