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

(1) Find $({C}_{R}B)∪A$;

(2) Given set $C=\{x|a < x < a+1\}$, if $C⊆B$, find the set of values that the real number $a$ can take.

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