Let $X$ be a projective variety over an algebraically closed characteristic $0$ field $\mathbb{K}$, and let $\Omega^\bullet_X$ be the de Rham sheaf of complexes of $\mathcal{O}_X$-modules of algebraic differential forms on $X$. Let $\mathbf{R}\Gamma\Omega^\bullet_X$ be (a complex representing) the derived gloval sections of $\Omega^\bullet_X$, and let $End(\mathbf{R}\Gamma\Omega^\bullet_X)$ be the total complex of hom-bicomplex $Hom(\mathbf{R}\Gamma\Omega^\bullet_X,\mathbf{R}\Gamma\Omega^\bullet_X)$.

Is $End(\mathbf{R}\Gamma\Omega^\bullet_X)$ quasi-isomorphic to $End(H^\bullet(X;\mathbb{K}))$as differential graded Lie algebras? (where the latter has trivial differential).