
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 $\{a\_n\}$ be a sequence of positive terms with first term $1$, and satisfying the recurrence relation $(n+1)a_{n+1}^{2}-na_{n}^{2}+a_{n+1}a_{n}=0 (n∈\mathbb{N}^{*})$. By induction, we conjecture the general formula for this sequence is $\_\_\_\_\_\_$.

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