Normally, you should keep many competing beliefs with associated levels of belief in them. The mindset of choosing the action with estimated best expected utility doesn't apply, as actions are mutually exclusive, while mutually contradictory beliefs can be maintained concurrently. Even when you consider which action to carry out, all promising candidates should be kept in mind until moment of execution.
Good point, I edited my form of the argument to include 'sets of beliefs'. If having a set of beliefs maximizes your utility, then having the set is what you "should" do, I think, in the spirit of the argument.
It has been claimed on this site that the fundamental question of rationality is "What do you believe, and why do you believe it?".
A good question it is, but I claim there is another of equal importance. I ask you, Less Wrong...
What are you doing?
And why are you doing it?