
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
In a space with 1989 points, no three of which are collinear, divide these points into 30 groups with distinct numbers of points in each group. If a triangle is formed by choosing one point from each of any three different groups, what should the number of points in each group be to maximize the total number of such triangles?

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