
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 lesson, 29 seventh graders attended, some of whom brought one ball each. During the lesson, sometimes one seventh grader would give their ball to another seventh grader who did not have a ball.

At the end of the lesson, $N$ seventh graders said, "I received balls less often than I gave them away!" Find the largest possible value of $N$, given that no one lied.

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