
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
Let $M$ be a non-empty set, and $#$ be an operation on it. If the following conditions are satisfied:
(Ⅰ) For any elements $a$, $b$, $c$ in $M$, $(a#b)#c=a#(b#c)$;
(Ⅱ) For any two elements $a$, $b$ in $M$, $a#b \in M$.
Then $M$ is said to be closed under the operation $#$.
Among the following sets, which are closed under both addition and multiplication operations?
① $\{-2, -1, 1, 2\}$  
② $\{1, -1, 0\}$  
③ $\mathbb{Z}$  
④ $\mathbb{Q}$.

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