
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 spring round of the 2000 Cities Tournament, high school students in country $N$ were presented with six problems. Each problem was solved by exactly 1000 students, but no two students together solved all six problems. What is the minimum possible number of high school students in country $N$ who participated in the spring round?

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