  Here we develop a new strategy to analyze the chemical freeze-out of light
(anti)nuclei produced in high energy collisions of heavy atomic nuclei within
an advanced version of the hadron resonance gas model. It is based on two
different, but complementary approaches to model the hard-core repulsion
between the light nuclei and hadrons. The first approach is based on an
approximate treatment of the equivalent hard-core radius of a roomy nuclear
cluster and pions, while the second approach is rigorously derived here using a
self-consistent treatment of classical excluded volumes of light (anti)nuclei
and hadrons. By construction, in a hadronic medium dominated by pions, both
approaches should give the same results. Employing this strategy to the
analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at
$\sqrt{s_{NN}} =2.76$ TeV and by STAR at $\sqrt{s_{NN}} =200$ GeV, we got rid
of the existing ambiguity in the description of light (anti)nuclei data and
determined the chemical freeze-out parameters of nuclei with high accuracy and
confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the
temperature $T = 175.1^{+2.3}_{-3.9}$ MeV, while at STAR energy there is a
single freeze-out of hadrons and nuclei at the temperature $T = 167.2 \pm 3.9$
MeV. We argue that the found chemical freeze-out volumes of nuclei can be
considered as the volumes of quark-gluon bags that produce the nuclei at the
moment of hadronization.
