Activity: Cleanse the taint on Saidin.
Useful outcome: Saidin cleansed of Dark One's influence. Good opportunity to clean up Aes Sedai screw-ups.
Side effect: You go mad.

Activity: Invent new form of transportation, the Gravity Drive.
Useful outcome: Fast interstellar travel. Humanity's first real opportunity to explore new worlds.
Side effect: You and quite a few other people go mad.

Activity: Take a rest cure involving no creative output at all and no more than two hours of mental stimulation a day.
Useful outcome: Patriarchal domination of 19th-century psychiatry brought into sharp relief.
Side effect: It is not at all restful and you go mad.