def _invoke(customer_text: str) -> None:
    """Submit one customer turn to the graph and retain its latest state."""
    graph_input: dict[str, Any] = {"messages": [HumanMessage(content=customer_text)]}
    if not st.session_state.started:
        graph_input.update(INITIAL_STATE)
        graph_input["messages"] = [HumanMessage(content=customer_text)]
        st.session_state.started = True

    try:
        result = st.session_state.graph.invoke(graph_input, config=st.session_state.config)
        st.session_state.agent_state = result
        flush_langfuse(st.session_state.handler)
    except Exception:
        st.session_state.started = bool(st.session_state.agent_state.get("messages"))
        st.error("The assistant could not process that request. Please try again.")