I need to follow the full progress of this project.
I need to track the full progress of this project.
都可以。
I need to trace all the process of this program.
trace 动词 跟踪 追踪
process 过程 进展
I must trace the all headway of the program.
I need to follow up the overall progress of the project.
follow up
v.
穷追, 把...探究到底, 用继续行动来加强效果