
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
A sequence of numbers arranged in a certain order is called a sequence, generally represented by $a_1, a_2, a_3, \ldots, a_n$, and can be briefly denoted as $\{a_n\}$. There is a sequence $\{a_n\}$ that satisfies a relation: $a_{n+1} = a_n^2 - na_n + 1$ (for $n=1, 2, 3, \ldots, n$), and $a_1 = 2$. Based on the given conditions, calculate the values of $a_2$, $a_3$, $a_4$, and then make an inductive conjecture about the expression for $a_n$ (expressed as an algebraic formula involving $n$).

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