
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 $U={$non-negative even numbers that are not greater than $10$}$, $A={0,2,4,6}$, and $B={x|x∈A,$ and $x < 4$}, find the complement of set $A$ within the universal set $U$ ($∁\_UA$) and the intersection of set $A$ and the complement of set $B$ within the universal set $U$ ($A∩(∁\_UB)$).

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