
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
In a modified sequence of numbers, the first number is \(1\), and for all \(n \geq 2\), the formula for the \(n\)-th number in the sequence changes so that \(a_{n+1} = \left(\frac{n+1}{n}\right)^3\). Calculate the sum of the third and the seventh numbers in this sequence.
A) \( \frac{106}{27} \)
B) \( \frac{134}{27} \)
C) \( \frac{145}{36} \)
D) \( \frac{171}{40} \)
E) \( \frac{221}{48} \)

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