Step 1: Crescents of gas tracking beneath the diaphragm on an erect chest film mean pneumoperitoneum, the radiological signature of a ruptured hollow viscus.
Step 2: Pair that with a rigid painful abdomen and shock numbers (tachycardia of 112 and hypotension of 80 systolic) and you have perforation peritonitis with circulatory compromise demanding surgery, not observation.
Step 3: After rapid fluid resuscitation the definitive move is emergency exploratory laparotomy to locate and close the leak. A stomach washout cannot fix a hole, a chest drain addresses the pleural space rather than free intraperitoneal gas, and doing nothing would be fatal.
\[\boxed{\text{Exploratory laparotomy}}\]