
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
(15) Given the following propositions:

(1) "If $x > 2$, then $x > 0$" - the negation of the proposition

(2) "For all $a \in (0, +\infty)$, the function $y = a^x$ is strictly increasing on its domain" - the negation

(3) "$π$ is a period of the function $y = \sin x$" or "$2π$ is a period of the function $y = \sin 2x$"

(4) "$x^2 + y^2 = 0$" is a necessary condition for "$xy = 0$"

The sequence number(s) of the true proposition(s) is/are _______.

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