
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 \(\{a_n\}\), \(a_1 = 1\), \(a_{n+1} > a_n\), and \(a_{n+1}^2 + a_n^2 + 1 = 2(a_{n+1}a_n + a_{n+1} + a_n)\), find \(a_n\).

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