
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
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?

Present the answer in LaTex format: \boxed{Your answer}
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