Which of the following steps is crucial in maintaining safety during a well shut-in?

Shutting the well in quickly after detection of a kick is a critical step in maintaining safety during a well shut-in. When a kick is detected, which indicates that formation fluids are entering the wellbore, rapid action is essential to prevent the escalation of the situation. Delaying the shut-in procedure can lead to a significant increase in pressure in the wellbore, potentially causing a blowout, which can result in catastrophic consequences.

Quickly shutting in the well allows for the immediate implementation of control measures, such as establishing barriers to prevent further influx of fluids and managing pressure. This action is paramount in ensuring the well is safely contained and helps to minimize risks to personnel, equipment, and the environment.

Other steps, while important in the overall process, do not provide the same direct immediate control needed in the event of a kick. Monitoring an influx or informing team members are crucial aspects of well control management but are secondary to the primary need for a swift shut-in to safeguard the well's integrity and mitigate danger.