
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
In the set of integers $Z$, the set of all integers whose remainder is $k$ when divided by 5 is called a "class $k$", denoted as \[k\], i.e., \[k\] = $\{x | x = 5n + k, n \in Z\}$, where $k = 0, 1, 2, 3, 4$. Now, consider the following four statements:  
① 2011 belongs to \[1\];  
② -4 belongs to \[4\];  
③ $Z = \[0\] \cup \[1\] \cup \[2\] \cup \[3\] \cup \[4\]$;  
④ For $a, b \in Z$, $a, b$ belong to \[k\] if and only if $a-b$ belongs to \[0\].  
Among these, the correct statement numbers are.

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