Did they attempt to after the US did so? If so, what were their shortcomings? If not, why did they not prioritize that as a symbolic loss in the Space Race?
hi! not discouraging other responses, but do check out responses these previous similar questions
When Apollo 11 landed on the moon, how far away were the Soviets from landing a man on the moon?
How was the Soviet space program affected after the United States went to the moon?
FYI, you may find more of interest in this section of the FAQ