-어/아 보도록 = -어/아 보다 (try, attempt to do something) + -도록
* -도록 is used to show 'purpose' of the following behavior.
e.g. 병원에 가 보도록 하세요. : Please try to go to a hospital. (or to see a doctor)
한국어를 배워 보도록 할게요. : I will try to learn Korean.
한국 음식을 먹어 보도록 할게요. : I will try to eat some Korean food.