  We present a new high-precision, JWST-based, strong lensing model for the
galaxy cluster Abell 2744 at $z=0.3072$. By combining the deep, high-resolution
JWST imaging from the GLASS-JWST and UNCOVER programs and a Director's
Discretionary Time program, with newly obtained VLT/MUSE data, we identify 32
multiple images from 11 background sources lensed by two external sub-clusters
at distances of ~160" from the main cluster. The new MUSE observations enable
the first spectroscopic confirmation of a multiple image system in the external
clumps. Moreover, the re-analysis of the spectro-photometric archival and JWST
data yields 27 additional multiple images in the main cluster. The new lens
model is constrained by 149 multiple images ($\sim66\%$ more than in our
previous Bergamini et al. 2023 model) covering an extended redshift range
between 1.03 and 9.76. The subhalo mass component of the cluster includes 177
member galaxies down to $m_{\rm F160W}=21$, 163 of which are spectroscopically
confirmed. Internal velocity dispersions are measured for 85 members. The new
lens model is characterized by a remarkably low scatter between predicted and
observed positions of the multiple images (0.43"). This precision is
unprecedented given the large multiple image sample, the complexity of the
cluster mass distribution, and the large modeled area. The improved accuracy
and resolution of the cluster total mass distribution provides a robust
magnification map over a $\sim\!45$ arcmin$^2$ area, which is critical for
inferring the intrinsic physical properties of the highly magnified, high-$z$
sources. The lens model and the new MUSE redshift catalog are released with
this publication.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics