  For the first time primary hot isotope distributions are experimentally
reconstructed in intermediate heavy ion collisions and used with
antisymmetrized molecular dynamics (AMD) calculations to determine density,
temperature and symmetry energy coefficient in a self-consistent manner. A
kinematical focusing method is employed to reconstruct the primary hot fragment
yield distributions for multifragmentation events observed in the reaction
system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. The reconstructed yield
distributions are in good agreement with the primary isotope distributions of
AMD simulations. The experimentally extracted values of the symmetry energy
coefficient relative to the temperature, $a_{sym}/T$, are compared with those
of the AMD simulations with different density dependence of the symmetry energy
term. The calculated $a_{sym}/T$ values changes according to the different
interactions. By comparison of the experimental values of $a_{sym}/T$ with
those of calculations, the density of the source at fragment formation was
determined to be $\rho /\rho_{0} = (0.63 \pm 0.03 )$. Using this density, the
symmetry energy coefficient and the temperature are determined in a
self-consistent manner as $a_{sym} = (24.7 \pm 1.9) MeV$ and $T=(4.9 \pm 0.2)$
MeV
