I thought I could convince them that I can/could balance

[EngLearner]

John wants to learn how to dance, so he asks his parents for permission to take dancing lessons in his free time after he's done with class in school. His parents don't approve of his decision and tell him that in his free time he should instead concentrate on his studies because they are more important than dancing. John is upset and he says the following in a conversation to a friend:

I want to learn how to dance. I asked my parents, but they didn't allow me to take dancing lessons. I thought I could convince them that I can/could balance dancing with school.

If at the time of speaking John believes that he can balance dancing with school, is it necessary for him to backshift "can" to "could", or would either option be correct in this case?

 

[emsr2d2]

If the whole story takes place in the past, use "could". If you're saying that you still think you can balance dancing with school, and that you previously tried to convince them of this, I'd use "can".