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We present a novel compartmental model to investigate the impact of mass testing, social distancing, and vaccination on the spread of COVID-19. To this end, we extend the well-known SIR model to account for incubation time, age-dependent symptom severity, inherent delays, and the counter measures themselves. Our main objective is to minimise the required social distancing while maintaining a hard infection cap. Using optimization-based control we find that an early and short lockdown is inevitable, but can then be relaxed monotonically. For real-life decision making we investigate the impact of the prediction horizon length on the optimal strategies. On short term it is optimal to vaccinate the high-risk group first whereas in the long run one should focus on people with highest contact rates.