
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. If $k > 0$, then the equation $x^2 + 2x - k = 0$ has real roots;
2. The negation of "If $a > b$, then $a + c > b + c$";
3. The converse of "The diagonals of a rectangle are equal";
4. The negation of "If $xy = 0$, then at least one of $x$ and $y$ is $0$".

Among these, the true propositions are __________.

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