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They are both right, but have a slight difference in emphasis. In English, we often express something in the *immediate* future by using the expression "to be going to" + verb. Just replace "am going to" with "will" and see what happens.
"I am going to sleep" = "I will sleep (very soon)" (This means you will sleep soon).
"I am going to go to sleep" = "I will go to sleep (very soon)" (This has a slight emphasis on the fact to you have to physically go somewhere in order to sleep).
Both in everyday usage, both are really very similar.
