
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
At a physical education class, 27 seventh graders attended, some of whom brought one ball each. Occasionally during the class, a seventh grader would give their ball to another seventh grader who did not have a ball.

At the end of the class, \( N \) seventh graders said: "I received balls less often than I gave them away!" Find the maximum possible value of \( N \) given that nobody lied.

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