Which of the following is a general indicator of narcotic use where reflex actions are diminished?

Depressed reflexes is the correct answer as it specifically refers to a physiological response that demonstrates diminished reaction times and altered neurological function commonly seen in individuals using narcotics. Narcotics, such as opioids, have a sedative effect on the central nervous system, leading to reduced reflex actions. This can manifest as slower or diminished responses to stimuli, indicating the drug's impact on the body’s normal reflex pathways.

While the other choices, such as drowsy, sluggish, and uncoordinated, might describe some behavioral or physical effects of narcotic use, they do not specifically measure the neurological impact in the same way that depressed reflexes do. Drowsiness indicates sleepiness and is a general symptom; sluggish refers to a lack of energy or slow movement but does not directly assess reflexes; and uncoordinated implies a lack of physical coordination, which can result from various factors, including but not limited to, narcotics. Thus, the focus on reflex actions makes "depressed reflexes" the most accurate indicator of narcotic use in this context.