
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
The sequence of natural numbers $a_{n}$ for $n = 1, 2, \ldots$ is such that $a_{1} = 1$ and $a_{n} = \frac{n+1}{n-1} \left(a_{1} + a_{2} + \ldots + a_{n-1}\right)$ for all $n = 2, 3, \ldots$. Find the formula for the "general term of the sequence", that is, a formula that explicitly expresses $a_{n}$ in terms of $n$ for any $n$.

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