A patient with a history of alcoholism and liver cirrhosis presents to the ED with diffuse abdominal pain, rigidity, and rebound tenderness. Labs show elevated WBC count and a lactate of 4 mmol/L. The patient has hypotension and tachycardia despite fluid resuscitation. Which immediate intervention is MOST appropriate for this patient?
Initiate broad-spectrum intravenous antibiotics.
Start the patient on oral lactulose for hepatic encephalopathy.
Perform an immediate diagnostic paracentesis.
Administer intramuscular analgesics for pain relief.