
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
Suppose a sequence $\{a_n\}$ satisfies the recurrence relation $a_{n+1}=a_n^2 - na_n + 1$ for $n=1, 2, 3, \ldots$, given that $a_1 = 2$. Deduce the general term formula for $a_n$ by calculating the values of $a_2$, $a_3$, and $a_4$.

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