If the haste spell is cast on a Bladesinging wizard, can the Bladesinger cast three cantrips in a turn using the Extra Attack feature?
For instance, say I'm a level 6 Bladesinging wizard, with haste already active. Can I do all of the following on the same turn?
- Cast booming blade to attack a target 5 feet from me
- Forego my second attack to cast shocking grasp
- (a) Use the additional action granted by haste to cast infestation
All 3 spells are cantrips.
Alternately, can I do steps 1 and 2 above, then:
- (b) use my additional action from haste to cast misty step (instead of infestation)
In this case, it's 2 cantrips and a bonus-action spell.
I've read a lot about reaction spells from War Caster, or Action Surge spells, or Quickened Spells from a sorcerer, but I haven't heard if it's ok to load up my turn with cantrips as a Bladesinger with haste, as per my 2 examples above.