The Grothendieck-Teichmüller group $\widehat{GT}$ acts on the genus $g$ mapping class group with $0$ or $1$ marked point

The goal of this article is to prove that the Grothendieck-Teichmüller group $\widehat{GT}$ acts on ${\widehat{\mathrm{\Gamma }}}_{g,0}$ and ${\widehat{\mathrm{\Gamma }}}_{g,1}$,the (full) profinite genus $g$ mapping class group with $0$ or $1$ marked point, for every $g>0$.