You are tasked with creating a Python class that models a Student with the attributes: name, and a list of scores for different subjects. This class should include methods to add a score, calculate the average score, and determine the grade based on the average.
The class should work as follows:
The Student class should be initialized with name (string). It should also have a scores attribute which is a list that stores the scores for different subjects.
The Student class should have a method add_score(self, score) that accepts a score (float) and adds it to the scores list.
The Student class should have a method average(self) that calculates and returns the average score of the student.
The Student class should have a method grade(self) that calculates the grade based on the average score and returns it.
Note: For the purposes of this exercise, you may assume that the grading system is as follows:
90 - 100
80 - 89
70 - 79
60 - 69
0 - 59
The program should execute all the commands properly and return the correct values.