
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
Calculate $a_2$ and $a_3$ for the sequence $\{a_n\}$ satisfying $a_1=1$, $a_{n+1} > a_n$, and $(a_{n+1}-a_n)^2-2(a_{n+1}+a_n)+1=0$. Then, find a general formula for $a_n$.

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