One of the best prayer someone can pray at the beginning of a new year is the prayer of Moses:
The LORD replied, “My Presence will go with you, and I will give you rest.”Then Moses said to him, “If your Presence does not go with us, do not send us up from here. How will anyone know that you are pleased with me and with your people unless you go with us? What else will distinguish me and your people from all the other people on the face of the earth?” And the LORD said to Moses, “I will do the very thing you have asked, because I am pleased with you and I know you by name.” (Exodus 33:14-17)

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