Final answer:
The recommended medication for a suspected opiate overdose with the symptoms described is Naloxone, an opiate antagonist that reverses opiate effects.
Step-by-step explanation:
Given the symptoms you describe — mumbling and slurring speech, incoherent sentences, extremely low blood pressure, slow heart rate, reduced respiratory rate, pinpoint pupils, and evidence of puncture sites on hands — the patient in question is likely experiencing an opiate overdose. The immediate administration of Naloxone is recommended in such situations. Naloxone is an opiate antagonist that rapidly reverses the effects of opiates, including respiratory depression which is a critical life-threatening aspect of opiate overdose.