
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. "In $\Delta ABC$, if $\sin A = \sin B$, then $A = B$" is a true proposition;
2. If a moving point $P$ has a total distance to two fixed points $F_1(-4,0)$ and $F_2(4,0)$ of $8$, then the trajectory of point $P$ is a line segment;
3. If $p \wedge q$ is a false proposition, then $p, q$ are both false propositions;
4. Let $x \in \mathbb{R}$, then "$x^2 - 3x > 0$" 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 conic section $\frac{x^2}{m} + y^2 = 1$ is $\frac{\sqrt{6}}{3}$;

Among these, the correct proposition numbers are ______.

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