J, 146 132 (Secretly breaks on certain answers)
n=:}:m=:|:".>{.`(<@}:@;@(1 2&{))`{:(`:0)"1;:;._2(1!:1)3 k=:3 :0 ')',~'(',','4}4j2 5j2":,(,.{:m)%.n ) echo'parallel'"_`k@.(*|-/ .*n)0 Parsing here is awful. I'm still trying to cook up a solution with ;:, but it may not happen tonight.
Edit: Realized that my output is basically broken, although it works for the examples given and parallels...
Edit: Posting the shorter version I already had. Probably not going to fix the output tonight.