
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
Consider the following propositions:
1. The converse proposition of "the diagonals of a rhombus bisect each other";
2. The set $\{x | x^2+1=0, x\in \mathbb{R}\}$ is empty or the set $\{0\}$ is empty;
3. For the proposition "p and q," if 'p' is false and 'q' is true, then "p and q" is false;
4. Having two equal sides and one interior angle of 60° is a necessary and sufficient condition for a triangle to be equilateral.
Among these, the true propositions are numbered __________.

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