
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
In the canteen, six dishes are offered to choose from. Each day, Vasya takes a certain set of dishes (possibly none), and this set of dishes must be different from all the sets he has taken on previous days. For how many maximum days can Vasya eat under these rules and what is the average number of dishes he will eat per day?

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