Noun-verb agreement for a list of singular nouns including "I" and joined by "or"

Question

I understand that when you have a list of singular nouns joined by "or", you should use a singular verb.

Example:

Either Chris or Len is the next player

But what verb do you use if one of the items in the list is "I"?

Either Justine or I is the next player

or

Either Justine or I am the next player

or something else?