Final answer:
The first action to take if a patient dislodges their tracheostomy tube is to assess their oxygen saturation and notify the healthcare provider, before taking further steps.
Step-by-step explanation:
When a patient with an uncuffed tracheostomy tube coughs violently during suctioning and dislodges the tracheostomy tube, the first action that a nurse should take is to assess the patient's oxygen saturation and notify the health care provider. Ensuring that the patient can breathe adequately and has sufficient oxygen is the top priority, and the oxygen saturation will provide immediate information regarding the patient's respiratory status. Following the assessment, additional measures such as reinserting the tube or ventilating the patient manually may be necessary depending on the patient's condition and the healthcare provider's guidance.