
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 non-empty set $S=\{x|m\leqslant x\leqslant l\}$ satisfy: when $x\in S$, then $x^2\in S$. Consider the following four statements:

1. If $m=1$, then $S=\{1\}$;
2. If $m=-\dfrac{1}{2}$, then $\dfrac{1}{4}\leqslant l\leqslant 1$;
3. If $l= \dfrac{1}{2}$, then $-\dfrac{\sqrt{2}}{2}\leqslant m\leqslant 0$;
4. If $l=1$, then $-1\leqslant m\leqslant 1$;

Among these, the correct ones are __________ (fill in the sequence numbers).

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