The word you're referring to is spelled 'segue'. The correct form in your example sentence would be 'segues', so "This answer segues into what I was going to say". Segue is derived from the Latin verb 'sequi', meaning "to follow".
What Is The Proper Spelling Of Sequeway, As In This Answers Sequeways Into What I Was Going To Say, As An Example.
I think it maybe segueways. Don't trust me though. Thanks for asking such a hot question babe =]