Group Actions · Hard problem

How many of these rules define an action of $(\mathbb Z_6,+)$ on $\mathbb Z_6$? $\;g\cdot x=x+g$; $\;g\cdot x=x-g$; $\;g\cdot x=x+1$; $\;g\cdot x=x+2g$; $\;g\cdot x=gx$.