I thought so too, only to see the correction suggesting that i should have written that he "goes to go to bed"!
Freeform Writing Exercise A1
It should be -
then he goes to bed
puis il va se coucher
The expression 'aller se coucher 'means 'to go to bed' not to go to go to bed if I have understood your query correctly.
To say I am going to go to bed it will be -
Je vais aller me coucher
or in the case of the cat -
Il va aller se coucher = he's going to go to bed
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