How do I get this while loop to execute the if statements by typing in certain strings/characters

Question

These are the steps I am stuck on in my programming assignment:

13. Create a while loop that will run until the user types in the exit command at the menu. a. After the loop print a goodbye message.
14. Within the loop determine which menu choice the user picked and do the appropriate action. The different possible actions are defined in the following steps. a. Don’t forget to take a new input from the user after you’ve processed their choice.

Here's my code I'm not sure what to change because when I input a character it won't display the if command it's assigned too.

import java.util.*;

public class Assignment5KJ
{
static Scanner scan = new Scanner(System.in);

public static void main(String[]args)
{
    Pet pet1 = new Pet("Fido", 3);
    Pet pet2 = new Pet("Furball", 1);
    Pet pet3 = null;

    System.out.println("Welcome to my pet store.");
    list(scan);


    do
    {            
        if(list(scan).equals("A"))
        {
            System.out.println(pet1.getName() + " is " + pet1.getAge() + " years old and " + pet1.getAdopt() + ".");
            System.out.println(pet2.getName() + " is " + pet2.getAge() + " year old and " + pet2.getAdopt() + ".");
            if (pet3 != null)
            {
                System.out.println(pet3.getName() + " is " + pet3.getAge() + " years old and " + pet3.getAdopt() + ".");
            }
            list(scan);
        }
        else if(list(scan).equals('B'))
        {
            pet1.setAge(3);
            pet2.setAge(1);
            list(scan);
        }
        else if(list(scan).equals("C"))
        {
            if(pet3 != null)
            {
                System.out.println("The pet store is full.");
            }
            else
            {
                System.out.println("Enter a name for the new pet");
                String name4 = scan.nextLine();
                System.out.println("Enter an age for the new pet");
                int age4 = scan.nextInt();
                Pet pet4 = new Pet(name4, age4);
                pet3 = pet4;
                System.out.println(pet4.getName() + " has been added to the store.");
            }                                                 
            list(scan);
        }

    }    
     while(!list(scan).equals("E"));

    System.out.println("Have a nice day.");
}

 public static String list(Scanner scan) {
    String list = "\n" + "A. List the pets in the store." +
            "\n" + "B. Age up the pets" +
            "\n" + "C. Add a new pet" +
            "\n" + "D. Adopt a pet" +
            "\n" + "E. Quit";
    System.out.println("Type the letter to make your selection." + list);
    scan = new Scanner(System.in);
    char selection = Character.toUpperCase((scan.next().charAt(0)));

    while (!(selection >= 'A' && selection <= 'E'))
    {
         System.out.println("Not a valid selection.");
         selection = Character.toUpperCase((scan.next().charAt(0)));
    }

    return selection + "";
}

public static boolean isValidInput(char selection) {
    return (selection >= 'A' && selection <= 'E');
}


}


public class Pet
{
    private String name;
    private int age;
    private boolean adoptStatus;

public Pet()
{
    name = "";
    age = 0;
    adoptStatus = false;
}

public Pet(String petName, int petAge)
{
    name=petName;
    age=petAge;
}

public void setName(String name1)
{
    name=name1;
}

public String getName()
{
    return name;
}

public void setAge(int age1)
{
    age = age1++;
}

public int getAge()
{
    return age;
}

public void Adopt()
{
    adoptStatus = true;
}

public boolean getAdopt()
{
    return adoptStatus;
}
}