Are these connected sentences correct (in terms of order)?

[PlacidRan]

Are these connected sentences correct (in terms of order - next, first, then)?

Jane cooked breakfast.
Next, she first dropped off Jamie at school.
Then she dropped off Carol.

 

[emsr2d2]

Are these connected sentences correct (in terms of order - next, first, then)?

Jane cooked breakfast.
Next, she first dropped off Jamie at school.
Then she dropped off Carol.

They're in the right order, but they don't sound natural. If you say "Next..." then you have already made it clear that the next thing she did was (therefore it was the first relevant thing she did after cooking breakfast).

Jane cooked breakfast, then she dropped first Jamie, then Carol, at school.