
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 $k$ when divided by 4 form a "class", denoted as $[k]$, i.e., $[k]=\{4n+k|n\in Z\}$, where $K=0, 1, 2, 3$. Given the following four statements: ① $2013\in[1]$; ② $-2\in[2]$; ③ $Z=[0]\cup[1]\cup[2]\cup[3]$; ④ If "integers $a, b$ belong to the same 'class'", then "$a-b\in[0]$".  
The number of correct statements is.

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