
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, where no three points are collinear, these points are divided into 30 groups with different numbers of points in each group. To maximize the total number of triangles formed by choosing one point from each of any three different groups as the vertices, how should the points be distributed among the groups?

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