
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:
$(1)$ "$m > 0$" is a necessary and sufficient condition for the equation $x^{2}+my^{2}=1$ to represent an ellipse;
$(2)$ "$a=1$" is a necessary but not sufficient condition for line $l_{1}$: $ax+y-1=0$ to be parallel to line $l_{2}$: $x+ay-2=0$;
$(3)$ "Function $f(x)=x^{3}+mx$ is monotonically increasing" is a necessary and sufficient condition for "$m > 0$";
$(4)$ "Given $p$ and $q$ are two nonequivalent propositions, "$p$ or $q$ is a true proposition" is a necessary but not sufficient condition for "$p$ and $q$ are true propositions".
Find the serial number(s) of all true propositions.

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