Final answer:
The proper response is to begin CPR and administer naloxone if the sleeping pills were opioids, while awaiting emergency medical services. Reassess the woman's pulse and breathing regularly and continue providing support as needed.
Step-by-step explanation:
In this case of a 26-year-old woman who has taken an overdose of sleeping pills and is now unresponsive with abnormal breathing, the next step after providing two rescue breaths and checking for rapid but weak pulse would be to begin CPR (cardiopulmonary resuscitation), specifically chest compressions. Given that she is showing signs of having a pulse, it's crucial to maintain circulation and provide artificial ventilation to ensure oxygen supply to the brain.
If available, it would also be appropriate to use naloxone (Narcan) given that the sleeping pills could be opioids, which suppress breathing. Naloxone can temporarily reverse an opioid overdose and should be administered as soon as possible, then continue providing support with rescue breaths and chest compressions until emergency medical services arrive.
Additionally, while waiting for medical help, it's vital to regularly reassess her pulse and breathing, and continue CPR as needed. Being prepared to provide first aid and contacting emergency services right away are essential steps in responding to an overdose situation.