
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 the sets of consecutive integers $\{1\}$, $\{2, 3\}$, $\{4,5,6\}$, $\{7,8,9,10\}$, $\ldots$, where each set contains one more element than the preceding one, and where the first element of each set is one more than the last element of the preceding set, let $S_n$ be the sum of the elements in the nth set. Find $S_{30}$.

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