using value for a function from another function

I am developing a manufacturing process flow and I am stuck in place where there is a loop. Any kind of help is greatly appreciated.

Stage 1 uses an input which is the output of stage 2 and also stage 2 uses 2 inputs which are the outputs of stage 1. Either one of the stage can occur first. The output just depends on the fraction of total input. mathematically it is written as, STAGE 1: y1+y2+y3 = x1+x2+x3 STAGE 2: x2+x3+x5 = y3+y5+y6

Having problem in coding this phase.

Thanks John