Action of algebraic group is smooth

Question

Let $k$ be a field and $X$ be a $k$-variety (separated of finite type), let $G$ be a smooth algebraic group over $k$ acting on $X$ $$a \colon G \times_k X \longrightarrow X$$ I am needing a reference that this action morphism is smooth. There is a post here which gives a simple proof but I am writing a document and I need to cite it from a precise reference. Thanks in advance.