The neutron skin thickness $Delta r_{rm{np}}$ of heavy nuclei is essentially determined by the symmetry energy density slope $L({rho })$ at $rho_c = 0.11/0.16rho_0$ ($rho_0$ is nuclear saturation density), roughly corresponding to the average density of finite nuclei. The PREX collaboration recently reported a model-independent extraction of $Delta r^{208}_{rm{np}} = 0.29 pm 0.07$ fm for the $Delta r_{rm{np}}$ of $^{208}$Pb, which suggests a rather stiff symmetry energy $E_{rm{sym}}({rho })$ with $L({rho_c }) ge 55$ MeV. We demonstrate that the $E_{rm{sym}}({rho })$ cannot be too stiff and $L({rho_c }) le 73$ MeV is necessary to be compatible with (1) the ground-state properties and giant monopole resonances of finite nuclei, (2) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, (3) the largest neutron star (NS) mass reported so far for PSR J0740+6620, (4) the NS tidal deformability extracted from gravitational wave signal GW170817 and (5) the mass-radius of PSR J0030+045 measured simultaneously by NICER. This allow us to obtain $55 le L({rho_c }) le 73$ MeV and $0.22 le Delta r^{208}_{rm{np}} le 0.27$ fm, and further $E_{rm{sym}}({rho_0 }) = 34.5 pm 1.5$ MeV, $L({rho_0 }) = 85.5 pm 22.2$ MeV, and $E_{rm{sym}}({2rho_0 }) = 63.9 pm 14.8$ MeV. A number of critical implications on nuclear physics and astrophysics are discussed.
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