
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 The negation of the proposition "If $b^2-4ac<0$, then the equation $ax^2+bx+c=0$ ($a\neq0$) has no real roots";
② The converse of the proposition "In $\triangle ABC$, if $AB=BC=CA$, then $\triangle ABC$ is an equilateral triangle";
③ The contrapositive of the proposition "If $a>b>0$, then $3a>3b>0$";
④ The converse of the proposition "If $m>1$, then the solution set of $mx^2-2(m+1)x+(m-3)>0$ is $\mathbb{R}$".

Among these, the true propositions are numbered \_\_\_\_\_\_.

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