
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 universal set be $\mathbb{R}$, and let the sets $A=\{x|x^2-9x+18\geq0\}$, $B=\{x|y= \frac{1}{\sqrt{x+2}}+\log(9-x)\}$.  
(1) Find $A\cup B$, $(\mathbb{R}\setminus A)\cap B$;  
(2) Given $C=\{x|a<x<a+1\}$, if $C\subseteq B$, find the range of the real number $a$.

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