
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:<br/>① The locus of points equidistant from the fixed point $\left(2,3\right)$ and the fixed line $2x-y-1=0$ is a parabola;<br/>② Let $A$ and $B$ be two fixed points, and $k$ be a positive constant. If $|PA|-|PB|=k$, then the locus of the moving point $P$ is a hyperbola;<br/>③ For any real number $\alpha$, the line $x\sin \alpha +y\cos \alpha =1$ always tangents a fixed circle;<br/>④ In the plane, the locus of points whose sum of distances to two fixed points is a constant is an ellipse.<br/>The correct proposition number is ______.

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