
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
Given 2000 points on a circle, starting from one point labeled with the number 1, move clockwise to the second point and label it with the number 2. Continue this process such that from the point labeled with number \( n \), move clockwise \( n \) points to label the next point with the number \( n+1 \). Continue this process until the points are labeled from 1 to 1993. Some points may be labeled with more than one number, and some points may not be labeled at all. What is the smallest number present on the point labeled with 1993?
(11th Annual American Invitational Mathematics Examination, 1993)

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