
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
Divide $n$ stones into two heaps randomly and record the product of the number of stones in the two heaps. Then, divide one heap into two heaps and record the product of the number of stones in these two heaps. Repeat this process with one of the three heaps, recording the product of the number of stones in the two heaps each time. Continue this process until there are $n$ heaps, each with one stone. Find the sum of these recorded products.

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