
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 $\{1\}$, $\{2, 3\}$, $\{4, 5, 6\}$, $\{7, 8, 9, 10\}$, $\cdots$, where each set contains one more element than the preceding one and starts with the element one more than the last element of the preceding set. Let $S_n$ be the sum of the elements in the nth set. Find the value of $S_{15}$.
- **A)** 1620
- **B)** 1695
- **C)** 1770
- **D)** 1960
- **E)** none of these

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