We present a new strong lensing (SL) model of the Hubble Frontier Fields (HFF) galaxy cluster Abell 2744, at z0.3072, by exploiting archival Hubble Space Telescope (HST) multiband imaging and Multi Unit Spectroscopic Explorer (MUSE) follow-up spectroscopy. The lens model considers 90 spectroscopically confirmed multiple images (from 30 background sources), representing the largest secure sample for this cluster field prior to the recently acquired James Webb Space Telescope (JWST) observations. The inclusion of the substructures within several extended sources as model constraints allowed us to accurately characterize the inner total mass distribution of the cluster and the position of the cluster critical lines. We included the lensing contribution of 225 cluster members, 202 of which are spectroscopically confirmed. We complemented this sample with 23 photometric member galaxies that are identified with a convolution neural network methodology with a high degree of purity. We also measured the internal velocity dispersion of 85 cluster galaxies, down to m(F160W)22, to independently estimate the role of the subhalo mass component in the lens model. We investigated the effect of the cluster environment on the total mass reconstruction of the cluster core with two different mass parameterizations. We considered the mass contribution from three external clumps, either based on previous weak lensing studies, or extended HST imaging of luminous members around the cluster core. In the latter case, the observed positions of the multiple images were better reproduced, with a remarkable accuracy of 0. '' 37, a factor of similar to 2 smaller than previous lens models, which exploited the same HST and MUSE data sets. As part of this work, we developed and made publicly available a Strong Lensing Online Tool (SLOT) to exploit the predictive power and the full statistical information of this and future models, through a simple graphical interface. We plan to apply our new high-precision SL model to the first analysis of the Grism Lens-Amplified Survey from Space-JWST-Early Release Science (GLASS-JWST-ERS) program, specifically to measure the intrinsic physical properties of high-z galaxies from robust magnification maps.