  A further development of the evolutionary picture of A+A collisions, which we
call the integrated HydroKinetic Model (iHKM), is proposed. The model comprises
a generator of the initial state GLISSANDO, pre-thermal dynamics of A+A
collisions leading to thermalization, subsequent relativistic viscous
hydrodynamic expansion of quark-gluon and hadron medium (vHLLE), its
particlization, and finally hadronic cascade ultrarelativistic QMD. We
calculate mid-rapidity charged-particle multiplicities, pion, kaon, and
antiproton spectra, charged-particle elliptic flows, and pion interferometry
radii for Pb+Pb collisions at the energies available at the CERN Large Hadron
Collider, $\sqrt{s} = 2.76$ TeV, at different centralities. We find that the
best description of the experimental data is reached when the initial states
are attributed to the very small initial time 0.1 fm/c, the pre-thermal stage
(thermalization process) lasts at least until 1 fm/c, and the shear viscosity
at the hydrodynamic stage of the matter evolution has its minimal value,
$\eta/s = \frac{1}{4\pi}$. At the same time it is observed that the various
momentum anisotropies of the initial states, different initial and relaxation
times, as well as even a treatment of the pre-thermal stage within just viscous
or ideal hydrodynamic approach, leads sometimes to worse but nevertheless
similar results, if the normalization of maximal initial energy density in most
central events is adjusted to reproduce the final hadron multiplicity in each
scenario. This can explain a good enough data description in numerous variants
of hybrid models without a prethermal stage when the initial energy densities
are defined up to a common factor.
