
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
There are 6000 points inside a circle, none of which are collinear.
1. Can this circle be divided into 2000 regions, each containing exactly three points? If so, how can it be divided?
2. If the distances between any two points in each region are integers and do not exceed 9, considering triangles formed with these three points as vertices, what is the minimum number of identical triangles among these triangles?

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