
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 sets $A=\{x|1\leq x<6\}$, $B=\{x|3<x<9\}$.  
(1) Find $(\complement_U A) \cup (\complement_U B)$;  
(2) Given $C=\{x|x-a-1<0\}$, if $B \subseteq C$, find the set of values for the real number $a$.

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