
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
A set of several numbers, none of which are the same, has the following property: the arithmetic mean of some two numbers in this set is equal to the arithmetic mean of some three numbers in the set and is also equal to the arithmetic mean of some four numbers in the set. What is the smallest possible number of numbers in such a set?

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