
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
Each of the 10 students came up with 5 natural numbers. It turned out that each number was thought up by at least three students. What is the largest possible number of different numbers that could have been thought of?

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