
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 containing 1989 points, none of which are collinear, we divide them into 30 groups with different numbers of points in each group. By taking one point from each of any three different groups to form a triangle, what should the number of points in each group be in order to maximize the total number of such triangles?

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