  We present results of simulations of directed flow of various hadrons in
Au+Au collisions at collision energies of $\sqrt{s_{NN}}=$ 3 and 4.5 GeV.
Simulations are performed within the model three-fluid dynamics (3FD) and the
event simulator based on it (THESEUS). The results are compared with recent
STAR data. The directed flows of various particles provide information on
dynamics in various parts and at various stages of the colliding system
depending on the particle. However, the information on the equation of state is
not always directly accessible because of strong influence of the afterburner
stage or insufficient equilibration of the matter. It is found that the
crossover scenario gives the best overall description of the data. This
crossover EoS is soft in the hadronic phase. The transition into QGP in Au+Au
collisions occurs at collision energies between 3 and 4.5 GeV, at baryon
densities $n_B \geq 4 n_0$ and temperatures $\approx 150$ MeV. In-medium
effects in the directed flow of (anti)kaons are discussed.
