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You can solve puzzles together, helping each other finding clues and talk about theories you have for solving the puzzles. Some of the easier ones are solvable by individuals, while other are easier in small groups. You will also see puzzles that are very hard to do, just look at what Funcom did with it's ARG's and you know what I am talking about.
You can group up to take down one of the dungeons in the game, there will be 8 or 9 of them at launch, with three difficulties for the ones you see first and two for the ones you get to see last. Here Funcom have left out most of the trash mobs so you spend most of your time on the interesting fights. The hardest difficulty requires you to progress horizontally to get the right gear and abilities for that particular dungeon or boss.
You can do open world group content that consists of multiple lairs spread around the world with hard-ass mobs that drops pieces of a puzzle that you can use to spawn bosses. Again you need to progress horizontally, getting gear and abilities to take down the bosses.
There are also world bosses in every zone, I haven't heard too much about what Funcoms intention with these are, but I think they are just meant as a challenge, not for gearing. Might be wrong here
There are several minigames for those who like those, all of them faction based, which should be interesting, so FvFvF. (I haven't researched this part so much)
There is at launch supposed to be one persistant area which also brings three factions up against each other. The kicker here is that there are several objectives each faction can hold and each of these objectives gives a faction wide buff. It will be interesting to see how being persistant will affect how this one works and how the buff affects the hardest mode for the dungeons.
What I like about this content is that it looks like there is enough different group content that even with the content they have at launch, I probably wouldn't see the same content for over a week. One day I could take a few dungeons, the next I could try to farm pieces to summon my very own boss, get my ass handed to me in Persistant PvP, but helping my faction out or trying to solve one of the hard puzzles.
To me, it looks like TSW will have a very solid "endgame" which to me looks very varied and allows casual and hardcore players to play in the same game due to the horizontal progression. It also looks like content added after launch could be added pretty seamlessly. For instance, you might get additonal puzzle quests or monster lairs in existing zones.