Revise input_select list during run

I am trying to create a dashboard, where the input is a class, and some properties of this class is being updated by user. This class for example initialized without any "scenario" and then user adds several scenarios.
At some point, I want the user be able to select one of the created scenarios from drop-down menu.

I have simulated the situation here. I have a list X that has two items ['math','physics']. But by running the dashboard, one element is added to the list as 'chemistry' . However the "ui.input_selec" doesn't follow this, and only show the ['math','physics'].

from shiny import App, ui, render, reactive

X = ["math","physics"]

app_ui = ui.page_fluid(
                       ui.input_select("course",'Select A course', X ),

def server(input, output, session):

    def append_list():
        print("adding item to the list")
    def print_list():
        return X

app = App(app_ui, server)

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