WI: Leonard Wood and what comes next

In the 1920 Republican primaries, Leonard Wood was looking to be the nomination, however Warren Harding managed to get the nomination as a darkhorse and win an easy election...then die 2 and half years in and Coolidge becomes. But what if Wood got the nomination, and the presidency? Let's assume the deaths of everyone until 1933 remain constant. Let's assume in this scenario Wood wins re-election. As Leonard Wood died in 1927, if he's still in office then who he'd choose as his vice president would be pretty eventful. Who'd do you think Wood would pick as his vice president that would end up inheriting his presidency(either in 1924 or he keeps his old veep)? How might that impact the Great Depression, or do you think a Wood presidency would stop that from happening?
 
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