2005 Austrian Mathematical Olympiad Final Round-Part 1/Problem 5

Problem

Find all real solutions $(a,b,c,d,e,f)$ of the system $4a = (b+c+d+e)^4, 4b = (c+d+e+f)^4, \dots 4 f = (a+b+c+d)^4.$

Use the concept of without loss of generality to create an order relation between $a,b,c,d,e,f.$