The two claims that most fully develop the speaker's argument in the passage are:
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Exploring space "brought tangible benefits that improve our lives in countless ways." (Paragraph 2)
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After nearly a quarter-century, "It is time for America to take the next steps" with space travel. (Paragraph 3)
These claims highlight both the advantages of space exploration and the need for ongoing efforts in this area, which are central to the speaker's argument.