
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
Design a new mathematical sequence where the first number is 1, and, for all \( n \geq 2 \), the sum of the first \( n \) numbers in the sequence is \( n(n+1) \). Determine the sum of the third and fifth numbers in the new sequence.
- **A)** \( 10 \)
- **B)** \( 14 \)
- **C)** \( 16 \)
- **D)** \( 18 \)
- **E)** \( 20 \)

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