
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, the correct one is \_\_\_\_\_\_ (write the serial number)  
① The negation of the proposition "There exists $x_0 \in \mathbb{R}$, such that $x_0^2+1>3x_0$" is "For all $x \in \mathbb{R}$, $x^2+1 \leq 3x$";  
② For the function $f(x) = \cos^2(ax) - \sin^2(ax)$, having a minimum positive period of $\pi$ is a necessary but not sufficient condition for "$a=1$";  
③ $x^2+2x \geq ax$ holds for all $x \in [1,2]$ if and only if $(x^2+2x)_{\min} \geq (ax)_{\max}$ holds for all $x \in [1,2]$;  
④ In $\triangle ABC$, "A > B" is a necessary and sufficient condition for "$\sin A > \sin B$".

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