A three-year-old girl with a history of illness has been vomiting and has diarrhea. She appears pale and tired with vital signs of BP 90/50, P 133, R 36. What is your next step?

In this scenario, the three-year-old girl is showing signs of dehydration and possible shock due to her vomiting, diarrhea, and vital signs indicating low blood pressure and high pulse rate. The priority in managing a pediatric patient, especially one presenting with these symptoms, is to ensure adequate oxygenation.

Applying high concentration oxygen is crucial because the child may be experiencing metabolic imbalances or inadequate perfusion due to fluid loss. By providing supplemental oxygen, you're supporting her respiratory system, which is especially vital given her pale and tired appearance, indicating possible hypoxia.

This step is essential before other interventions like starting intravenous fluids or administering medications, as maintaining adequate oxygen levels can stabilize her condition during transport.

Therefore, focusing on oxygen delivery is the most immediate and life-saving action in this situation, making it the correct choice for the next step in the management of this child.