To follow up, I searched for the phrase "small manageable tasks". I found the following: Roy Johnson's 1993 book on Revisions and Examinations: Guidance Notes for Students, p. 31 advises students to "break down"" their work into "small manageable tasks" because that would give students more confidence. Barron's Guide to Medical & Dental Schools also suggests this approach and then gives the advice to "solve the small tasks in a prioritized manner." The popular book on Managing Your Mind (Oxford: Oxford University Press, 1995) speaks of the "Salami technique", meaning that you "set yourself small manageable tasks so that by progressing through them you will eventually accomplish the large task." And the phrase "to divide the plan into small, manageable tasks" is more frequent after 1995. Thus Peter A. Darnell advises programmers in 1996 to use "stepwise refinement" or to "divide a large problem into small, manageable tasks." The first time I encountered the phrase was in a 1970 book on C-System Principles of Operations.
In other words, it looks even less likely that the passage: "The secret of getting ahead is getting started. The secret of getting started is breaking your complex overwhelming tasks into small manageable tasks, and then starting on the first one.” is a genuine quote.
Most people will probably not be bothered by the pretense of attributing the passage to a famous author. I am!