"Mangio la propria torta."
Since "strictly" is also given as an option, what's wrong with my translation: "I strictly eat the cake"? I would have translated it the way you have it, but didn't think it was correct without "mia" after "la".
I made a sentence with the words that were given. The person may be on a cake eating diet and does not stray from its requirements and therefore, strictly eats cake, va bene?