
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 1989 points in space, no three of which are collinear, divide them into 30 groups with each group containing a different number of points. If you form triangles by taking one point from each of three different groups, determine the distribution of the number of points in each group in order to maximize the total number of such triangles.

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