Brain Game: Increasing Reductions

Starting with the given O, add the letter provided in the next line and rearrange the existing letters (if necessary) to form a new word in each set of blanks, continuing all the way to REDUCTIONS.  Good luck:

O +D = _ _ +S = _ _ _ +E = _ _ _ _ +C = _ _ _ _ _ +N = _ _ _ _ _ _ +R = _ _ _ _ _ _ _ + I = _ _ _ _ _ _ _ _ + T = _ _ _ _ _ _ _ _ _ + U = R E D U C T I O N S

Here is one SOLUTION.

ONE SOLUTION:

O >
DO >
SOD >
DOSE >
CODES >
SECOND >
SCORNED >
CONSIDER >
DOCTRINES >
REDUCTIONS

NOTE: Some entries could be other words using the same letters. For instance, DOSE could be ODES or DOES. If your list was markedly different, feel free to post it in the comments.