
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 inverse proposition of "In $\Delta ABC$, if $A=B$, then $\sin A = \sin B$" is true.
2. If a moving point $P$ has a total distance of 8 from two fixed points $F_1(-4,0)$ and $F_2(4,0)$, then the trajectory of point $P$ is the line segment $F_1F_2$.
3. If $p \wedge q$ is a false proposition, then both $p$ and $q$ are false propositions.
4. For $x \in \mathbb{R}$, "$x^2 - 3x > 0$" is a necessary but not sufficient condition for "$x > 4$".
5. If the real numbers $1, m, 9$ form a geometric sequence, then the eccentricity of the ellipse $\frac{x^2}{m} + y^2 = 1$ is $\frac{\sqrt{6}}{3}$.

The correct proposition numbers are __________.

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