
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 \(\{a_n\}\) defined by
\[ a_1 = 0, \quad a_{n+1} = a_n + 4 \sqrt{a_n + 1} + 4 \quad (n \geq 1), \]
find \(a_n\).

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