how can i show her ive changed?

i want to show my gf who is close to breaking up with me that ive changed from the liar i am (i never cheated or flirted with another girl) to a trust worthy person, people have said that actions speak louder then words but i dont know how to show her, shes loves me less then she did before and i want to show her i have changed. what can i do to show her she can trust me again so then she can see this could be a new start to our relationship