
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 \(\{x_n\}\) defined by \(x_0 = 0\) and \(x_{n+1} = x_n + a + \sqrt{b^2 + 4ax_n}\) for \(n = 0, 1, 2, \ldots\), where \(a\) and \(b\) are given positive real numbers, find the general term of this sequence.

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