The circulatory system includes the blood, blood vessels (e. g. capillaries), and the heart, which pumps blood through the blood vessels to all the parts of your body. explain how the digestive system and circulatory system work together to bring nutrients to all the cells in your body.

When the food reaches the small intestine it was absorbed by the villi present in it ! after absorption it reaches the blood where the food(glucose) mixes with plasma and reaches to different organthere the food via capillaries and then via lymph reaches the cell and thus there further oxidation takes place.

so that was the path !!!

That would be a working theory.