Adding element to the list on keypress and clearing the list

As in topic my job is to do a code where user writes some text into textbox and when user hits enter key, the text from the textbox should be added to ul list under Things header.
I added also reset button but it’s not working because adding elements to list isn’t working but I think it should work when I will fix it. I don’t know where I made mistake. Could anyone help me or give me advice what should I do?

<!DOCTYPE html>
<html>
<head>
    <title>List</title>
</head>
<body>
    <h1 id="title">List</h1>

    <form>
        <input type="text" id="user-todo" placeholder="List" required>
    </form>

    <h2 id="todo-header">Things</h2>
    <ul id="list">

    </ul>
    <button id="clear">Reset</button>
    <script>
        var input = document.getElementById("user-todo");
        input.addEventListener("keyup", function(event) {
            if (event.keyCode === 13) {
                event.preventDefault();
                // what happens when user hits ENTER
                $(document).ready(function() {
                    $('ul').append("<li>"+($('#user-todo').val()) + "</li>");
                });
            }
        });

        function clear() {
            document.getElementById("list").innerHTML = '';
        }
    </script>
</body>

</html>