Final answer:
The spinocerebellar tract is the pathway that conveys proprioceptive and cutaneous information to the cerebellum for movement coordination.
Step-by-step explanation:
The spinal tract that ascends to the cerebellum and relays information from cutaneous and proprioceptive organs is the spinocerebellar tract. This tract is responsible for carrying proprioceptive information, which is the sensory input that provides feedback on the position of body parts in space, to the cerebellum for the coordination of movement and posture. The other tracts mentioned serve different purposes: the anterolateral spinothalamic tract relays pain and temperature, the dorsal column-medial lemniscus pathway carries fine touch, vibration, and proprioception, and the corticospinal tract is mainly involved in carrying motor commands from the brain to the muscles.