
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 the set $M$ consist of all integers that can be represented as the difference of squares of two integers. Consider the following statements:  
① All odd numbers belong to $M$.  
② If an even number $2k$ belongs to $M$, then $k \in M$.  
③ If $a \in M$ and $b \in M$, then $ab \in M$.  
④ If we arrange all positive integers not belonging to $M$ in ascending order into a sequence, then the sum of the first $n$ terms of this sequence, $S_n$, belongs to $M$.  
Among these statements, the correct ones are. (Write down the numbers of all correct statements)

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