
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 a classroom, there are ten students. Aline writes ten consecutive integers on the board. Each student chooses one of the ten integers, such that no two students choose the same integer. Each student then calculates the sum of the nine integers chosen by the other nine students. Each student whose result is a perfect square receives a gift.

What is the maximum number of students who will receive a gift?

A perfect square is an integer of the form \( n^2 \), where \( n \) is a natural number.

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