It's not so much that you need to reduce your accent but that you must acquire a different accent, the one that happens to be mainstream. I don't know if that helps, but that is what a linguist would say. Everyone has an accent. It is just a matter of which is considered standard.

It seems like it would be hard for someone new to a language to even discern an accent. You have my congratulations for even becoming conversant in more than one language. I took several years of Spanish and still cannot carry on a conversation or read much of anything in it.