
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 $A=\{x|1\leqslant x\leqslant 5\}$ and $B=\{x|\log_{2}x > 1\}$,
(1) find $A\cap B$ and $(∁_{R}B)\cup A$;
(2) Given the set $C=\{x|2a-1\leqslant x\leqslant a+1\}$, if $C\subseteq A$, find the range of values for the real number $a$.

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