
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 school is hosting a Mathematics Culture Festival, and it was recorded that on that day, there were more than 980 (at least 980 and less than 990) students visiting. Each student visits the school for a period of time and then leaves, and once they leave, they do not return. Regardless of how these students schedule their visit, we can always find \( k \) students such that either all \( k \) students are present in the school at the same time, or at any time, no two of them are present in the school simultaneously. Find the maximum value of \( k \).

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