Final answer:
The two viruses that can promote cancer development are Human immunodeficiency virus (HIV) and Adenovirus, as they can interfere with cell cycle regulation and have associations with certain lymphomas, leukemia, and potentially other human cancers.
Step-by-step explanation:
Among the listed viruses, the two that have the potential to promote cancer development due to the nature of their life cycles in the infected cell are Human immunodeficiency virus (HIV) and Adenovirus. Oncogenic viruses are capable of causing cancer by interfering with normal cell cycle regulation, either by introducing oncogenes or inhibiting tumor suppressor genes. HIV is associated with several types of lymphoma and T-cell leukemia. On the other hand, while not all adenoviruses are oncogenic, some types have been implicated in the development of human cancers. Adenoviruses can transform cells in vitro and some are associated with human cancers, although a direct causative relationship in humans is less clear compared to other well-established oncogenic viruses such as HPV.