
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 universal set $R$, set $A=\{x|x\leqslant 3\text{ or }x\geqslant 6\}$, and set $B=\{x|-2 < x < 9\}$.

1. Find $A\cup B$ and $(∁_{R}A)\cap B$.
2. Given set $C=\{x|a < x < a+1\}$, if $C\subseteq B$, find the range of values for the real number $a$.

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