
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
During recess, $n$ students sit in a circle around their teacher to play a game. The teacher distributes candy to the students in a clockwise direction according to the following rules: first, the teacher selects a student and gives them one piece of candy. The teacher then skips over one student and gives the next student one piece of candy, skips over two students and gives the next student one piece of candy, skips over three students and gives the next student one piece of candy, and so on. Determine the value of $n$ such that eventually (possibly after passing through many rounds) each student has at least one piece of candy.

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