There are several different terms that can be used as synonyms for "system of reckoning Gregorian calendar." Some possible options include "Gregorian dating system," "Gregorian calendar counting method," and "Gregorian era calculation system." Other potential terms that could be used include "Gregorian timekeeping system," "Gregorian calculation methodology," and "Gregorian annual tracking method." Regardless of the specific term used, all of these phrases refer to the same basic idea of using the Gregorian calendar as a means of calculating dates and keeping track of time. This system was introduced in the late 16th century and is still widely used around the world today.