
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
Given the following four propositions:  
① The negation of the proposition "For any $x \in \mathbb{R}$, $x^2 \geq 0$" is "There exists an $x_0 \in \mathbb{R}$, such that $x_0^2 \geq 0$";  
② The negation of "There exists an $x_0 \in \mathbb{R}$, such that $x_0^2 - x_0 > 0$" is: "For any $x \in \mathbb{R}$, $x^2 - x < 0$";  
③ For any $x \in [-1, 2]$, $x^2 - 2x \leq 3$;  
④ There exists an $x_0 \in \mathbb{R}$, such that $x_0^2 + \frac{1}{x_0^2 + 1} \leq 1$.  
Among these, the true propositions are numbered \_\_\_\_\_\_ (fill in the numbers of all true propositions).

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