
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 a non-negative sequence $\left\{a_{n}\right\}(n \geqslant 1)$ with the first term $a$, and the sum of the first $n$ terms $S_{n}$, where $S_{n}=\left(\sqrt{S_{n-1}}+\sqrt{a}\right)^{2}$ for $n \geqslant 2$. If $b_{n}=\frac{a_{n+1}}{a_{n}}+\frac{a_{n}}{a_{n+1}}$, find the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$, denoted as $T_{n}$.

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