
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 $n$ balls, divide them into two groups arbitrarily and calculate the product of the number of balls in each group. Continue by dividing one of the groups into two groups arbitrarily and calculate the product again, repeating this process until no further division is possible. What is the sum of all these products?

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