
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 domain of the function $f(x) = \frac{\sqrt{2x^2+1}}{\sqrt{5-x}} + \sqrt{x-2}$ be the set $A$, and let $B=\{x|-3<x-4<4\}$, $C=\{x|x<a-1 \text{ or } x>a\}$.  
(1) Find $A$ and $(\complement_R A) \cap B$;  
(2) If $A \cup C = \mathbb{R}$, find the range of the real number $a$.

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