In the continuous-cycle program, the start and stop push buttons control an internal ___________ instruction, which in turn starts and stops the sequence.

In a continuous-cycle program, the start and stop push buttons trigger an internal coil instruction. Coils are fundamental elements in programmable logic controllers (PLCs) that represent outputs or control actions. When the start button is pressed, the coil is energized, allowing the program to execute certain operations; conversely, when the stop button is pressed, the coil is de-energized, stopping those operations.

Using coils enables the setting and resetting of states within the program, which is essential for managing a sequence of actions in a continuous process. The relationship between the push buttons and the coil allows for real-time control over the automation process, facilitating the desired start and stop functions efficiently.

In contrast, timers and counters serve different purposes—timers manage delays and time-based operations, while counters track the count of events. Relays, while similar in concept to coils, are not programmable and are typically used in hardware rather than software control structures. Therefore, the coil instruction is the most appropriate answer for managing the sequence in a continuous-cycle program through direct control via push buttons.