Learn English – phrase meaning “to progress through an outlined set of steps/time”

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How do you refer to a person continuing along an outlined path through time? Specifically, what do you call the actual action of progressing from the earlier stages to the later/older stages?

I'm trying refer to the path a person takes through college (year 1, then 2, then 3, etc.), and what you would call the act of going through those steps/ progressing to the later ones.

The sentence I'm trying to complete is "it is common for students to do this as they _____." It needs to mean something like "progress through their years at school" or "get older", but "older/aging" only in reference to them rising through the grades. I just don't know how to say that in a shorter, more concise manner instead of literally stating "progress through their time at school".
I know there has to be some better phrase that means "the act of someone moving through this specifically outlined set of time".

Best Answer

The word "advance" is currently used in this way.

Oxford Dictionaries offers this definition, marked 1.1:

advance : Make or cause to make progress

An example sentence: "Michael advanced from third to fourth grade."

When progression is marked by a series of steps, this is the most common word used to describe progression through the steps in my experience.