
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
What is the sum of all distinct products of each pair of numbers chosen from the set $\{1, 2, 3, \ldots, n\}$, including the pairs $(1 \cdot 2), (1 \cdot 3), \ldots, (1 \cdot n), (2 \cdot 3), (2 \cdot 4), \ldots, ((n-1) \cdot n)$?

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