
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 that the terms of the sequence \(\left\{a_{n}\right\}\) are all positive numbers and \(S_{n}\) is the sum of its first \(n\) terms. For any positive integer \(n\), the arithmetic mean of \(a_{n}\) and 2 is equal to the geometric mean of \(S_{n}\) and 2. Find the general term of this sequence.

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