
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 a set $A$, if for any $a, b \in A$, it holds that $a+b \in A$ and $a-b \in A$, then the set $A$ is called a closed set. Consider the following four statements:  
① The set $A=\{-4, -2, 0, 2, 4\}$ is a closed set;  
② The set $A=\{n|n=3k, k\in \mathbb{Z}\}$ is a closed set;  
③ If sets $A_1$ and $A_2$ are closed sets, then $A_1 \cup A_2$ is a closed set;  
④ If sets $A_1$ and $A_2$ are closed sets, and $A_1 \subseteq \mathbb{R}, A_2 \subseteq \mathbb{R}$, then there exists $c \in \mathbb{R}$, such that $c \notin (A_1 \cup A_2)$.  
Among these, the correct statement(s) is/are \_\_\_\_\_\_.

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