TOEFL Grammar Question

[tajansu]

This is the grammar exercise that I am working on now.
According to the Constitution, the Congress shall assemble on the first Monday in December unless they shall by law appointment a different day.

The correct answer should be-- by law appoint a different day. What's the part of speech of "appoint" in the sentence? Why do we use "appoint"?

Thank you.

[Alan]

verb