
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
Consider the sequence $\{a\_n\}$ that satisfies $a_{n+1}=a_n^2-na_n+1$, where $n=1$, $2$, $3$, $...$, $a_1=2$. By finding the values of $a_2$, $a_3$, $a_4$, conjecture a general formula for $a_n$.

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