
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 $U=\mathbb{R}$, set $A=\{x|x < -4 \text{ or } x > 1\}$, and set $B=\{x|-3\leqslant x-1\leqslant 2\}$,
(1) Find $A∩B$ and $(∁_{U}A)∪(∁_{U}B)$;
(2) If set $M=\{x|2a\leqslant x < 2a+2\}$ is a subset of set $A$, find the range of values for the real number $a$.

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