
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 four propositions:
1. If the inverse of a proposition is true, then its negation must be true;
2. In an arithmetic sequence $\{a_n\}$, where $a_1=2$, and $a_1$, $a_3$, $a_4$ form a geometric sequence, then the common difference is $-\frac{1}{2}$;
3. Given $a > 0$, $b > 0$, and $a+b=1$, then the minimum value of $\frac{2}{a} + \frac{3}{b}$ is $5+2\sqrt{6}$;
4. In $\triangle ABC$, if $\sin^2A < \sin^2B+\sin^2C$, then $\triangle ABC$ is an acute triangle.
The correct proposition numbers are __________ (Fill in the numbers of the propositions you think are correct).

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