
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
Let set $M$ be a non-empty set of numbers that satisfies the following conditions:<br/>($i$) $2\in M$;<br/>($ii$) For any $x\in M$ and any $y\in M$, $x-y\in M$;<br/>($iii$) For any $x\in M$ and $x\neq 0$, $\frac{1}{x}\in M$.<br/>Given the following four conclusions:<br/>①$0\in M$;<br/>②$1\notin M$;<br/>③For any $x$ and $y\in M$, $x+y\in M$;<br/>④For any $x$ and $y\in M$, $xy\in M$.<br/>The correct conclusions are______.

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