Please let me know what is the standard notation for group action.

I saw the following three notations for group action. (All the images obtained as G\acts X for different deinitions of \acts.)

(1)

I saw this one most, but only in handwriting and I like it. But I did not find a better way to write it in LaTeX.

\usepackage{mathabx,epsfig}
\def\acts{\mathrel{\reflectbox{$\righttoleftarrow$}}}

(2)

It is almost as good as 1, but in handwriting this arrow can be taken as $G$.

\usepackage{mathabx}
\def\acts{\lefttorightarrow}

(3)

I saw this one in print, I guess it is used since there is no better symbol in "amssymb".

\usepackage{amssymb} 
\def\acts{\curvearrowright}