
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 a sequence of positive terms $\{a\_n\}$ with the first term $a\_1=1$, and for all positive integers $n$, the following equation holds: $(n+1)a_{n+1} - na\_n^2 + (n+1)a\_n a_{n+1} - na\_n = 0$. Find the general term formula for the sequence $\{a\_n\}$, denoted as $a\_n =$ \_\_\_\_\_\_.

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