  We present a new strong lensing (SL) model of the Hubble Frontier Fields
galaxy cluster Abell 2744, at z=0.3072, by exploiting archival Hubble Space
Telescope (HST) multi-band imaging and Multi Unit Spectroscopic Explorer (MUSE)
follow-up spectroscopy. The lens model considers 90 spectroscopically confirmed
multiple images (from 30 background sources), which represents the largest
secure sample for this cluster field prior to the recently acquired James Webb
Space Telescope observations. The inclusion of the sub-structures within
several extended sources as model constraints allows us to accurately
characterize the inner total mass distribution of the cluster and the position
of the cluster critical lines. We include the lensing contribution of 225
cluster members, 202 of which are spectroscopically confirmed. We also measure
the internal velocity dispersion of 85 cluster galaxies to independently
estimate the role of the subhalo mass component in the lens model. We
investigate the effect of the cluster environment on the total mass
reconstruction of the cluster core with two different mass parameterizations.
We consider 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 are better reproduced, with a remarkable accuracy of 0.37", a
factor of $\sim2$ smaller than previous lens models. We develop and make
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
high-precision SL model to the first analysis of the GLASS-JWST-ERS program,
specifically to measure the intrinsic physical properties of high-$z$ galaxies
from robust magnification maps.
