Derived $\pi$-length of a $\pi$-solvable group in which the Sylow $p$-subgroups are either bicyclic or of order $p^3$

The group is called a bicyclic group if it is the product of two cyclic subgroups. It is proved that the derived $\pi$-length of the $\pi$-solvable groups in which the Sylow $p$-subgroups are either bicyclic or of order $p^3$ for any $p\in\pi$ is at most 7 and if $2\not\in\pi$ then the derived $\pi$-length is at most 4.