
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
Group positive integers as follows: $(1), (2,3), (4,5,6), (7,8,9,10), \cdots$, where each group has one more number than the previous group, and the first number of each group is 1 greater than the last number of the previous group. Let $S_{n}$ denote the sum of the numbers in the $n$-th group. Determine the value of $S_{21}$.

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