
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 $[k]$, then $[k] = [5n+k]$, where $k=0, 1, 2, 3, 4$. Among the following statements, the correct ones are:  
① $2013 \in [3]$  
② $Z = [0] \cup [1] \cup [2] \cup [3] \cup [4]$  
③ "Integers $a, b$ belong to the same 'class'" is a necessary and sufficient condition for "$a - b \in [0]$"  
④ The statement "If integers $a, b$ satisfy $a \in [1], b \in [3]$, 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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