cant advance in QUEST on (path to GIRUVEGAN)

You should be able to teleport to the gate crystal in the Golmore Jungle or Eruyt Village. Either one you teleport to, make your way south in Golmore Jungle. Look at your map, in the part called "The Rustling Chapel" is the path to the Feywood. Go in and explore. South some more is the gate to Giruvegan.

If you're talking about the puzzle part, go to any of the "star" shaped areas on your map ("Ice Field of Clearsight", and "The Edge of Reason") stand in the middle of the structures, and you should be able to press "X" on atleast one of them. Stand there, and rotate your camera with the right joystick, look for the "path" that looks like a forest. Just follow it straight until you get to another structure, and do the same until you get to the next screen.

If you've already figured that out, and trying to get into the door to Giruvegan, you have to summon Belias, then try opening it again. This can only be done if you do the part I explained in the second paragraph in "The Edge of Reason". Good luck!

I know I'm not the best at explaining stuff, so you could always try Gamefaqs or Gamespot. Crap load of guides.