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Train with Lyx. 


If you somehow haven't met Lyx and are asking about powers.
You need to go to the outskirts (map where the farm is)
Click the explore icon and go North > West > South

Pay attention to what she says and go there, when you go to the place and get what you were looking for open your inventory and check the item.

After you're done you should have the Cottage icon appear in the map.

With that you can train magic with her and unlock powers.