
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 the proposition: For any \(x \in \{x | -2 < x < 4\}\), \(|x-2| < 3\). \\
(4) \(\triangle > 0\) is the 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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