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

The GLASS-JWST Early Release Science Program. III. Strong lensing model of Abell 2744 and its infalling regions