  A model is presented that simultaneously describes shape coexistence and
quadrupole and octupole collective excitations within a theoretical framework
based on the nuclear density functional theory and the interacting boson model.
An optimal interacting-boson Hamiltonian that incorporates the configuration
mixing between normal and intruder states, as well as the octupole degrees of
freedom, is identified by means of self-consistent mean-field calculations
using a universal energy density functional and a pairing interaction, with
constraints on the triaxial quadrupole and the axially-symmetric quadrupole and
octupole shape degrees of freedom. An illustrative application to the
transitional nuclei $^{72}$Ge, $^{74}$Se, $^{74}$Kr, and $^{76}$Kr shows that
the inclusion of the intruder states and the configuration mixing significantly
lower the energy levels of the excited $0^+$ states, and that the predicted
low-lying positive-parity states are characterized by the strong admixture of
nearly spherical, weakly deformed oblate, and strongly deformed prolate shapes.
The low-lying negative-parity states are shown to be dominated by the deformed
intruder configurations.
