FATE Party Auto Group?

Is there not a way that we can auto group up in a FATE?

Eg, there is me and my choco, and then a lone tank participating in a FATE. I'm playing DPS, but my choco is healing. He cannot heal the tank, even though the tank is taking damage. Is there no way to allow us to automatically group up while participating in FATEs, or at least review the Choco AI to heal other players that aren't in my party?

Edit:
I think it would be a good idea, if there were, let's say 16 or more players participating, if the FATE recognised this, and an algorithm grouped up the players as close to a 2T-2H-4D ratio as possible, it would aid healers in contributions, it would help increase DPS due to party buffs, it would help tanks because healers would be able to target them easier.

The only drawback is if you were in a DF queue, you may get kicked since you're now in a party. This would need to be taken into consideration of course, maybe by having a specific 'FATE group' party that works alongside your standard party set up?

Just invite him to party...

Ok, and if he refuses the invite. I'm second on aggro table, he dies because I can't heal him, I get full aggro and then die because I'm not a tank. As good advice as "just invite him to party..." is, it requires him to actually accept the invite...

Unfortunately that's just the way it is. Some people don't want to accept party invites because they're grinding FATES while waiting for the Duty Finder to pop (though if they're a tank it should be nigh instant). I suggest packing a heal spell of your own that you can spam on whoever might need. My first (and main) class is Summoner so I didn't have the problem of being unable to heal or Raise people outside of a party but as I started leveling alt classes I found it frustrating to not have those skills anymore. Summoner honestly has it the best in solo play being able to have a three-man party (yourself, summon, Chocobo) to solo FATES and the like while also doing damage and keeping teammates alive if anyone else shows up.

Auto-grouping would be nice but I can see it easily becoming a problem with leechers being carried through FATES by virtue of standing within the blue area and being counted as part of the party even though they're not doing anything.