Help with Amine Synthesis

The reaction given is for the nucleophilic addition of a secondary amine to a ketone. Below is the mechanism for this acid catalyzed reaction:

The protonation of the hydroxyl group makes it a better leaving group.

The group replaces the halogen as the halogen is a better leaving group. Lithium aluminum hydride is a strong reducing agent. It takes nitrogen-nitrogen bonds and allows for nitrogen hydrogen bonds to be formed instead. A primary nitrogen is bonded to two hydrogens and one R group. After reduction, a primary amine is formed.