  Symmetry energy, temperature and density at the time of the intermediate mass
fragment formation are determined in a self-consistent manner, using the
experimentally reconstructed primary hot isotope yields and anti-symmetrized
molecular dynamics (AMD) simulations. The yields of primary hot fragments are
experimentally reconstructed for multifragmentation events in the reaction
system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. Using the reconstructed hot
isotope yields and an improved method, based on the modified Fisher model,
symmetry energy values relative to the apparent temperature, $a_{sym}/T$, are
extracted. The extracted values are compared with those of the AMD simulations,
extracted in the same way as that for the experiment, with the Gogny
interaction with three different density-dependent symmetry energy terms.
$a_{sym}/T$ values change according to the density-dependent symmetry energy
terms used. Using this relation, the density of the fragmenting system is
extracted first. Then symmetry energy and apparent temperature are determined
in a self consistent manner in the AMD model simulations. Comparing the
calculated $a_{sym}/T$ values and those of the experimental values from the
reconstructed yields, $\rho /\rho_{0} = 0.65 \pm 0.02 $, $a_{sym} = 23.1 \pm
0.6$ MeV and $T= 5.0 \pm 0.4$ MeV are evaluated for the fragmenting system
experimentally observed in the reaction studied.
