
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
Let $\left\{a_{n}\right\}$ be a sequence of positive terms with the first term being 1, and satisfying the recurrence relation $(n+1) a_{n+1}^{2} - n a_{n}^{2} + a_{n} a_{n+1} = 0$ for $n=1, 2, 3, \ldots$. Find the general term $a_{n}$.

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