Really, the best advice would be "Get out of Syracuse before the Romans show up" but I suppose your infuriating machine would refuse to transmit that as well.
Perhaps "Get off of Earth before Nemesis sends some more comets our way"
Nemesis: http://en.wikipedia.org/wiki/Nemesis_%28star%29
Reasoning: The Roman invasion could have been predicted, but wouldn't have been well supported by evidence -- although foreign invasions were certainly a repeated (even cyclic) phenomenon. Of course, the Nemesis hypothesis rests on an unproven root cause of all major extinction events, whereas invasions came from various, known causes...
4[anonymous]
Hey, all you have to do is think of an analogous suggestion today. I'm afraid I lack the historical knowledge necessary to even attempt to provide direct advice...
A possible problem would that there would be no analogous situation. That there is no place for your country to get out of before some people show up. I don't know if communicating similarly important abstract ideas works, and how much your correctness or incorrectness of advice matters...
Really, the best advice would be "Get out of Syracuse before the Romans show up" but I suppose your infuriating machine would refuse to transmit that as well.