
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 $A=\{ x|3\leqslant 3^{x}\leqslant 27\}$, $B=\{ x|\log_{2}x > 1\}$.  
$(1)$ Find $A\cap(\complement_{R}B)$;  
$(2)$ Given the set $C=\{ x|1 < x < a\}$, if $C\cap A=C$, find the set of values for the real number $a$.

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