
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 $A=\{x|2x^{2}-x-6\geqslant 0\}$, and set $B=\{x|\log_{2}x\leqslant 2\}$.

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

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