
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 $\left[k\right]$, that is, $\left[k\right]=\{5n+k\left|\right.n\in Z\}$, where $k=0$, $1$, $2$, $3$, $4$. Four conclusions are given as follows:<br/>①$2015\in \left[0\right]$;<br/>②$-3\in \left[3\right]$;<br/>③$Z=\left[0\right]\cup \left[1\right]\cup \left[2\right]\cup \left[3\right]\cup \left[4\right]$;<br/>④"Integers $a$ and $b$ belong to the same 'class'" is necessary and sufficient condition for "$a-b\in \left[0\right]$". The correct conclusions are ____.

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