
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
Among the following propositions: ① For all $x \in \mathbb{R}$, $x^2 \geq x$; ② There exists an $x \in \mathbb{R}$ such that $x^2 \geq x$; ③ $4 \geq 3$; ④ The necessary and sufficient condition for "$x^2 \neq 1$" is "$x \neq 1$ or $x \neq -1$". Among these, the correct proposition numbers are.

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