On a spherical Earth model with a radius of 6,371 kilometers, two cities, A and B, lie on the equator and are separated by an angle of 45 degrees. City C lies directly north of city A by 1,000 kilometers. Find the spherical distance from city C to city B in kilometers. Express your answer in the simplest radical form. Let's think step by step and output the final answer within \boxed{}.
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