tl;dr

1. Find the co-relation between variables in the LFSR equation
   1. d == out (75%)
   2. a == b (75%)
   3. c^d == out (75%)
   4. (d!= out) => (c==1) always
2. Solve for the seed using 2000 output bits
3. Try out which among the four possible combinations decrypt the flag