The EF of the PEN wavefunction just derived naturally lends itself to a mixed quantum-classical treatment in the spirit of the analogous approach derived for the electron-nuclear problem. Here, we aim to treat on equal footing the photonic and the nuclear degrees of freedom, by introducing the idea of photon-nuclear trajectories, whereas the electrons are described quantum mechanically. Therefore, we will now briefly describe how the CTMQC algorithm can be easily extended to the PEN problem in Section II A, and we will test it in Section III on two model case studies of dynamical processes in the strong light-matter coupling regime.