Dumbledore can simply reach into that pouch to grab what he needs.

what is the point of a belief that does not allow you to make predictions that you are willing to stand by

The route from mental phenomena to actions does not have to pass through explicitly modeling and making predictions about the world. You can just have beliefs that function as simple heuristics for making actions without any modeling or prediction at all.

and planned this all

I find this highly unlikely. Hermione should have some concept by now of how destabilizing an effect her apparent death would have on Harry. I don't think she'd have the heart to knowingly deceive him like this.

I have to write it somewhere - because what is the point of a belief that does not allow you to make predictions that you are willing to stand by - and I guess this is the place. I believe that Hermione is not dead (duh!), and planned this all for the purposes of getting Harry out of his debt to Malfoy and/or preventing herself from being used as a weapon against Harry. She used or was discovered by Fred and George who were subsequently memory charmed by Dumbledore, who has spent entirely too much time off-camera of late.

Edit: I'll add that - on the odd chance I'm right, and this ends up sounding like bragging - I don't think that makes me particularly clever; I think it speaks to skillful but subtle hinting on the part of the author.