During the germinal period, the first task of the zygote's outer cells is

The answer is "implantation". The germinal period is the first two weeks after conception. As the zygote forms and grows by cell division, the differentiation of cells results in the inner layer of cells or blastocyst that becomes the embryo while the outer layer or trophoblast, will provide nutrients and support. The implantation of the fertilized egg into the lining of the uterus provides those nutrients. Note that many pregnancies are lost during this time - this is a period when most women are not even aware of the pregnancy.