寝ると眠る=Fall Asleep?

From Twitter:
A. What time did you go to bed?
B. Dunno–2?
A. Why do ya look tired?
1. B. I didn’t __ until 3.
2. A. __ to sleep later then?
But lack of sleep reduces memory, memory organization, brain cleansing and testosterone–even testicle size!
B. Yeah?
A. Yup!

Choose:
a. go to sleep
b. fall asleep

Answers and Explanation:
1. b., fall asleep, which means to slip into the brain-rest-state of unconsciousness
2. a., go to sleep, which means to (sometimes to go to the bed and to) try to fall into the brain-rest-state of unconsciousness