SILK-ROAD 2020 Problem 4

Prove that for any natural number $m$ there exists a natural number $n$ such that any $n$ distinct points on the plane can be partitioned into $m$ non-empty sets whose convex hulls have a common point. The convex hull of a finite set $X$ of points on the plane is the set of points lying inside or on the boundary of at least one convex polygon with vertices in $X$ , including degenerate ones, that is, the segment and the point are considered convex polygons. No three vertices of a convex polygon are collinear. The polygon contains its border.