
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 sets $A=\{x|3\leqslant x < 6\}$ and $B=\{x|2 < x < 9\}$.

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

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