
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, $n$ ($n \geq 2$) students are seated in a circle with a teacher. The teacher distributes candies in a counterclockwise direction according to the following rules: 
- First, they select a student and give them one candy.
- Skip one student and give the next student a candy.
- Skip two students and give the next student a candy.
- Skip three students and give the next student a candy.
- This pattern continues.

Determine the value of $n$ such that eventually (possibly after many rounds), every student has at least one candy.

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