
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 the sequence \(\left\{a_{n}\right\}\) such that \(a_{1} = 0\) and \(a_{n+1} = a_{n} + 1 + 2 \sqrt{1+a_{n}}\) for \(n = 1, 2, \ldots\), find \(a_{n}\).

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