<human>: I need some help figuring out how the euro rail pass system works.

Im going to Europe this summer. I start off in Amsterdam then go to paris and then down to Barcelona. What I would like to do is buy a eurorail pass for the bullet trains that would let me ride from amsterdam to belgium to paris and possibly to england.

but not in that order. Im meeting some people in paris and while im leaving after a 4 day stay in amsterdam to go to paris several people have put interest in to riding the train to amsterdam for the day.

so my trip schedule would possible look like amsterdam to belgium, belguim to paris. 

paris to belguim, paris to amsterdam

then maybe paris to the uk.

Could you distill the essence of the text into 1-3 sentences?
<bot>: Is there a europass that will let me ride the bullet train multiple times in a short period(roughly 2 weeks) between france, belguim, the netherlands and england?