I'm writing about a project I worked on in my PS. The project started in August and I joined in October. So which verb should I use here?
The project had _______ for 2 months before I joined the team.
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For calls for a timespan rather than a timepoint, so a perfect progressive construction works better than a simple perfect; and start would be very odd, since it ordinarily designates a single event, not a process†:
The project had been running for two months before I joined the team.
Without the for you can use start and indicate a timepoint two months earlier:
The project had started two months before I joined the team
† There are contexts in which start can take a progressive—The project was just starting when I joined—but a 'start' lasting two months suggests the project was floundering badly before you arrived!