Final answer:
The U.S. federal authorities attempted to deal with the 'Indian problem' through the signing of treaties and the policy of Americanization.
Step-by-step explanation:
The U.S. federal authorities attempted to deal with the 'Indian problem' in two main ways. The first was through the signing of treaties with Native American tribes. These treaties guaranteed tribes protection on federal Indian reservations, payment for lands, money for schools, and support in establishing Western farming practices. However, these treaties were often violated by land-hungry White settlers. The second method was through the policy of Americanization, which aimed to assimilate Native peoples into mainstream American culture. This policy included efforts to terminate tribal sovereignty, promote English language and education, and relocate Native populations to urban areas.