Before the fellowship of the ring broke and Frodo and Sam decide to go on alone, Gandalf lead the group. I've been wondering which way he meant for the group to choose into Mordor.

There seem to be only two known ones, Black Gate and Cirith Ungol. The Black Gate seems insurmountable, at least in the movies, and Gandalf, again in the movie, seemed shocked at the foresight of Frodo taking the path of Cirith Ungol. So I wonder what was his intention.