
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
Given a sequence of positive terms \(\left\{a_{n}\right\}\) that satisfies the following conditions:
1. \(a_1 = 2012\)
2. \(a_2\) and \(a_3\) are integers
3. The sequence \(\left\{n a_{n} - n^{2}\right\}\) is a geometric sequence with a common ratio not greater than 10

Find the general term formula of the sequence \(\left\{a_{n}\right\}\).

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