Is it something to do with refining the Zell, Quistis and Minotaur cards into Hyper Wrists, Samantha Souls and Adamantines respectively?

An athsma mind - Perhaps a reference to Zell and his occasional airheadedness?
Can help you find
A way to raise your strength - His card refines into Hyper Wrists, which teach the ability Strength+60%

When not alone - Perhaps a reference to the Brothers?
The power stone
My help you go a length - Minotaur's card refines into Adamantines (Power stone?) which teach Vitality+60%

Without ado
You can still grow
The power to call forth

With greater force
The fire source
And cold wind of the North - If we follow along with the same theory, this could mean refining the Quistis card into Samantha Souls, which teach SumMagic+40%.

It may be right off, but it's worth a shot.