"Do not forget your initiative mind, live up to your youth" means: Do not forget your initiative mind and his dream, stick to and work hard to do what he wants, don't waste his youth, and keep an optimistic attitude. Do not forget your initiative mind first appeared in Bai Juyi's Maitreya.
Most modern people are saying that they should stick to their ideals and work hard, which is described as not forgetting that your initiative failed his youth.