Hermit Druid does not have summoning sickness.You have no basic lands in library.
({5} magic symbol) ({G} magic symbol) ({U} magic symbol) ({U} magic symbol) your first turn, with ({5} magic symbol) ({U} magic symbol) ({U} magic symbol) available each other turn available.
Steps
Activate Hermit Druid by paying ({G} magic symbol) and tapping it, causing you to mill your library.
Cast Nexus of Fate by paying ({5} magic symbol) ({U} magic symbol) ({U} magic symbol) , causing you to take an extra turn after this one and shuffle Nexus of Fate into your library.
Move to your next turn, drawing Nexus of Fate during your draw step.