
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
Define a set $A$. If for any $a$ and $b$ belonging to set $A$, we have $a+b$ and $a-b$ also belonging to set $A$, we call set $A$ a closed set. The following are three conclusions: $①$ Set $A=\{-4,-2,0,2,4\}$ is a closed set; $②$ Set $B=\{n|n=3k, k\in Z\}$ 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. The serial number of the correct conclusions is \_\_\_\_.

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