
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 $A=\{x|y= \sqrt{x-3} - \frac{1}{\sqrt{7-x}}\}$, $B=\{y|y=-x^{2}+2x+8\}$, $C=\{x \in \mathbb{R}|x < a \text{ or } x > a+1\}$  
(1) Find $A$, $(\mathbb{R} \setminus A) \cap B$;  
(2) If $A \cup C = C$, find the range of values for $a$.

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