Step 1: Analyse options.
- Input-Output machine problems usually arrange words alphabetically or by length.
- The words in Step III are: in (2), play (4), role (4), schooling (9), vital (5).
- Looking at the alphabetical order: in, play, role, schooling, vital.
- By reversing the typical steps of a word-sorting machine, Option (b) provides the starting sequence that results in this Step III.
Step 2: Conclusion.
The definite input for this progression is "in role play vital schooling".
Final Answer: (b) in role play vital schooling