For some nonzero reals $$a,b$$, the numbers $$a+b, a-b, ab, \frac{a}{b}$$ form an arithmetical progression in that order. If $$a+b$$ can be expressed as $$\frac{x}{y}$$ where $$x$$ is an integer, $$y$$ is a positive integer, and $$x,y$$ are coprime, determine the value of $$|x+y|$$.