'Whose' is often the only reasonable option. Here is the usage note from the American Heritage Dictionary: 'It has sometimes been claimed that whose is properly used only as the possessive form of who and thus should be restricted to animate antecedents, as in a man whose power has greatly eroded. But there is extensive literary precedent for the use of whose with inanimate antecedents, as in The play, whose style is rigidly formal, is typical of the period.
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