7. Given two oblique lines $m, n$ in plane $\alpha$, where $m / / n$, the set of points in plane $\alpha$ that are at a distance $d$ from both lines $m, n$ could be: (1) a line; (2) a point; (3) two points; (4) an empty set. The correct answers are (write down all the correct answer numbers) $\qquad$ .
7. (2) (3) (4) Detailed explanation: The points at a distance $d$ from the line $m$ lie on the lateral surface of a cylinder with the line $m$ as its axis and a radius of $d$. The intersection of the cylinder with an inclined plane results in an ellipse. Therefore, the points in plane $\alpha$ that are at a distance $d$ from two lines $m, n$ depend on the value of $d$, which involves considering the intersection points of two ellipses. Hence, there can be one point, two points, or an empty set, choose (2)(3)(4).