
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: \\
(1) If $m > 0$, then the equation $x^{2}-x+m=0$ has real roots; \\
(2) The converse of the proposition "If $x > 1, y > 1$, then $x+y > 2$"; \\
(3) The negation of "For all $x$ in $\{x | -2 < x < 4\}$, $|x-2| < 3$"; \\
(4) $\Delta > 0$ is a necessary and sufficient condition for a quadratic equation $ax^{2}+bx+c=0$ to have one positive root and one negative root. \\
The true propositions are \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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