<s>[INST] The figure EFGH contains two parallel and equal chords, $\overline{EF}$ and $\overline{GH}$, in addition to two other non-parallel chords, $\overline{AB}$ and $\overline{CD}$, all inside the circle. Is it possible to assign two distinct points, $P$ and $Q$, on $\overline{EF}$ and on $\overline{GH}$ respectively, such that the number of intersection points of all the chords with the segment $\overline{PQ}$ is maximal?[/INST]