
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 \(a_1 = 1\) and \(a_{n+1} = 1 + a_n + \sqrt{1 + 4a_n}\) for \(n \in \mathbf{N}^*\), find the explicit formula for \(a_n\).

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