How are Regeneration, Faith, and Union with Christ ordered in Reformed Theology?

In the Reformed [*Ordo Salutis*](https://en.wikipedia.org/wiki/Ordo_salutis) , or order of salvation, how are Regeneration, Faith, and Union with Christ ordered? (Note that the order of salvation is a logical order, not temporal, and the believer will experience several stages concurrently.) Because of Total Depravity, the doctrine that we are spiritually dead in our sin, I think Regeneration is usually said to precede Faith, because we need to be brought back to spiritual life in order to have faith. Faith is said to precede Union with Christ because it is through Faith that the Holy Spirit unites us the Christ. But isn't it Union with Christ that gives us new life in Christ? Does Union with Christ therefore precede Regeneration? Or is the new life of Regeneration somehow different from the new life we receive through being united to Christ? How is this chicken-and-egg cycle resolved in Reformed Theology?