
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
In the sequence $\{a_n\}$, it is known that $a_1=1$, and when $n \geq 2$, $a_n - a_{n-1} = 2n - 1$. Calculate $a_2$, $a_3$, $a_4$ in turn, and then conjecture the expression for $a_n$.

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