
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 $a, b \in A$, both $a+b$ and $a-b$ belong to $A$, then $A$ is called a closed set. Consider the following three 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.

Identify the correct statement(s).

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