Final answer:
The reticular formation of the brain stem influences consciousness through the reticulospinal tract, which connects the reticular system with the spinal cord.
Step-by-step explanation:
The reticular formation of the brain stem influences levels of consciousness. The pathway responsible for this influence is the reticulospinal tract. This tract connects the reticular system, a region of gray matter in the brain stem, with the spinal cord. It influences trunk and limb muscles related to posture and movement, as well as muscle tone and autonomic functions.