Lost, 64 62 bytes

-2 bytes thanks to Wheat wizard

/%?"HeadsvU"-+@
^<<<<<<<</>>>>v
>%?"Tails^="-+\
^v%"Side?!">@"

Try it online!

I'll get the ball rolling with a relatively simple solution. This flips heads from 119 starting states, tails from 120, and side from 1.