
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
Calculate the value of \( S_{n}=(1 \cdot 2)+(1 \cdot 3)+\ldots+(1 \cdot n)+(2 \cdot 3)+(2 \cdot 4)+\ldots+(2 \cdot n)+\ldots+(n-1) \cdot n \).

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