  We present a simple generalisation of the $\Lambda$CDM model which on the one
hand reaches very good agreement with the present day experimental data and
provides an internal inflationary mechanism on the other hand. It is based on
Palatini modified gravity with quadratic Starobinsky term and generalized
Chaplygin gas as a matter source providing, besides a current accelerated
expansion, the epoch of endogenous inflation driven by type III freeze
singularity. It follows from our statistical analysis that astronomical data
favors negative value of the parameter coupling quadratic term into
Einstein-Hilbert Lagrangian and as a consequence the bounce instead of initial
Big-Bang singularity is preferred.
