Your personnel cannot gain skills while facing this dilemma. Unless you have Astrometrics, Intelligence, and Treachery or Geology, Honor, and Navigation, randomly select a personnel to be stopped and if this dilemma's owner discards an event from hand, then he or she may destroy an event.
"The cloak failed, and half the ship materialized in solid rock."
Image courtesy of trekcc.org
No copyright infringement intended