The Rulebook states:

“In tournament play, the active player takes as many sequential actions as desired (from zero to all possible actions) before pausing and indicating that the inactive player can take an action. The inactive player can then either perform an action or decline the opportunity. Then the active player can take more actions. If the inactive player passes, and then the active player passes, no more actions can be taken during that step (except for reactions to damage, as usual).”

What that means is the active player can use as many global abilities (in addition to purchasing dice, fielding characters, and using action dice) as they want during the Main Step, but the inactive player must be passed priority before they can use a global ability. When the inactive player is passed priority they can perform 1 action, then they must pass priority back to the active player who can again do as many actions as they want. When the inactive player uses no actions and passes priority back to the active player and the active player also takes no actions the step will end. Priority must be passed at the end of the Main Step and during the Attack step after blockers are declared, but before combat damage is assigned.