We report the discovery of an actinide-boost, very metal-poor ($\left[\mathrm{Fe/H} \right]=-2.38$), $r$-process-enhanced ($\left[\mathrm{Eu/Fe} \right]=0.80$) star, LAMOST J0804+5740, within the Gaia-Sausage-Enceladus (GSE). Based on the high-resolution ($R\sim36,000\; and \;60,000$) and high signal-to-noise ratio spectra obtained with the High Dispersion Spectrograph on the Subaru Telescope, the abundances of 48 species are determined. Its $\log\epsilon\rm(\mathrm{Th}/\mathrm{Eu}) = -0.22 $ establishes it as the first confirmed actinide-boost star within the GSE. Comparative analysis of its abundance pattern with theoretical $r$-process models reveals that the magnetorotationally driven jet supernova $r$-process model with $\hat{L}v$ = 0.2 provides the best fit and successfully reproduces the actinide-boost signature. Kinematic analysis of actinide-boost stars reveals that approximately two-thirds of them are classified as $\textit{ex-situ}$ stars, suggesting that actinide-boost stars are more likely to originate from accreted dwarf galaxies. As the first actinide-boost star identified within the GSE, J0804+5740 will provide valuable insights into $r$-process nucleosynthesis in accreted dwarf galaxies like the GSE, especially on the production of the heaviest elements.
Comment: 10 pages, 4 figures, and 3 tables