<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Master Boniface, a gingerbread maker, wanted to bring joy to as many children as possible, so he was constantly working when he was awake. If he slept too little, he worked drowsily. Sleeping too much made him feel sluggish, and he also had less time for work. He realized that the number of gingerbreads he could make per hour was proportional to the product of the duration of his sleep and wakefulness. How many hours per day should Master Boniface sleep in order to make the maximum number of gingerbreads? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
16
Master Boniface, a gingerbread maker, wanted to bring joy to as many children as possible, so he was constantly working when he was awake. If he slept too little, he worked drowsily. Sleeping too much made him feel sluggish, and he also had less time for work. He realized that the number of gingerbreads he could make per hour was proportional to the product of the duration of his sleep and wakefulness. How many hours per day should Master Boniface sleep in order to make the maximum number of gingerbreads?
test