
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 propositions:  
(1) The contrapositive of the proposition "If $m>0$, then the equation $x^2+2x-m=0$ has real roots";  
(2) "$x=1$" is a sufficient but not necessary condition for "$x^2-3x+2=0$";  
(3) The negation of the proposition "For all $x, y \in \mathbb{R}$, if $xy=0$, then $x=0$ or $y=0$" is "For all $x, y \in \mathbb{R}$, if $xy \neq 0$, then $x \neq 0$ and $y \neq 0$";  
(4) "$\neg p$" being true is a necessary but not sufficient condition for "$p \land q$" being false;  
(5) The negation of the universal proposition "For all $x \in \mathbb{R}$, $x^2+x+3>0$" is "There exists an $x \in \mathbb{R}$ such that $x^2+x+3 \leq 0$".  
Among these, the numbers of the true propositions are.

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