The two claims that most fully develop the speaker's argument in the passage are:
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Despite the successes brought by exploring space, "much remains for us to explore and to learn." (Paragraph 3)
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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 emphasize the need for continued exploration and the urgency to advance in space travel, which aligns with the overall argument of the passage advocating for further space exploration efforts.