
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 four propositions about conic sections:

1. Given points $M(-2,0)$ and $N(2,0)$, if $|PM|+|PN|=3$, then the locus of point $P$ is a line segment.
2. The distance from a focus of a hyperbola to one of its asymptotes is equal to the length of its imaginary semi-axis.
3. The hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$ and the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ have the same foci.
4. The two roots of the quadratic equation $x^{2}-mx+1=0 (m > 2)$ can respectively serve as the eccentricities of an ellipse and a hyperbola.

Determine the correct proposition(s).

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