
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 a sequence of sets of consecutive integers $\{1\}, \{2, 3\}, \{4, 5, 6\}, \{7, 8, 9, 10\}, \cdots$, where each set contains one more element than the previous set and the first element of each set is one greater than the last element of the previous set, find the sum $S_{21}$ of the elements in the $21$-st set.

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