
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 $\left\{x_{n}\right\}$ satisfying $x_{0}=0$ and $x_{n+1}=x_{n} + a + \sqrt{b^{2} + 4 a x_{n}}$ for $n=0,1,2,\cdots$, where $a$ and $b$ are given positive real numbers, find the general term formula for $x_{n}$.

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