Final answer:
The brain is the organ responsible for crucial functions such as sneezing, coughing, and regulating sleep, with the brainstem playing a key role in these reflex actions.
Step-by-step explanation:
The organ that plays a significant role in sleeping, sneezing, and coughing is the brain. The respiratory centers of the brain are responsible for controlling involuntary actions such as breathing, sneezing, and coughing. When it comes to sleeping, the brain is also central to regulating the sleep-wake cycle through different brain areas and neurotransmitters.
For instance, coughing often involves a reflex arc that starts with a stimulus in the respiratory tract and ends with the cough outburst, which is controlled by the brainstem. Similarly, sneezing is also triggered by an irritation in the nasal passage and is ultimately a reflex initiated by the brain.