
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
Translate the given propositions:
(1) The negation of the statement "If $x > 2$, then $x > 3$";
(2) The negation of "For all $a \in (0, +\infty)$, the function $y = a^x$ is monotonically increasing in its domain";
(3) "π is a period of the function $y = \sin x$" or "2π is a period of the function $y = \sin 2x$";
(4) "$x^2 + y^2 \neq 0$" is a necessary condition for "$xy = 0$";
Among these propositions, the true propositions are marked with the numbers ______.

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