
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 as the set of real numbers $\mathbb{R}$, and sets $A=\{x\mid 1\leqslant x\leqslant 3\}$, $B=\{x\mid x > 2\}$, $C=\{x\mid 1 < x < a\}$.

1. Find $A\cup B$ and $(∁_{R}B)\cap A$ respectively.
2. If $C\subseteq A$, find the range of values for $a$.

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