
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 $Z$, all integers that have a remainder of $k$ when divided by 5 form a "class", denoted as $[k]$, i.e., $[k]=\{5n+k|n\in Z\}$, where $k=0, 1, 2, 3, 4$. Then, the correct statements among the following are \_\_\_\_\_\_ (write down all correct numbers)  
① $2013\in[3]$;  
② $-1\in[3]$;  
③ $Z=[0]\cup[1]\cup[2]\cup[3]\cup[4]$;  
④ The necessary and sufficient condition for "integers $a, b$ belong to the same class" is "$a-b\in[0]$";  
⑤ The statement "For integers $a, b$ satisfying $a\in[1]$, $b\in[3]$, then $a+b\in[4]$" is true for both the original statement and its converse.

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