The delete statement conflicted with reference constraint "fkey$lc_action_value$action"
When trying to delete Automatic Action that has some Action Value applied (Calculations/Placeholders etc) from the Process Designer and save changes you will get the above error message.
The error comes from the fact that the action you try to delete (in table lc_action) is present as a reference attribute in table lc_action_value, hence the error about constraint.
Solution / Workaround:
Make sure you delete all modifications done on the Automatic Action first, save it, and then try to delete the Action itself.