
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 sequence $\{a\_n\}$ where all terms are positive, the sum of the first $n$ terms is $S\_n$, and it satisfies $a\_1=1$, $a_{n+1}=2 \sqrt {S_{n}}+1,n\in\mathbb{N}^{*}$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Suppose the sequence $\{b\_n\}$ satisfies $b_{n}= \frac {4n^{2}}{a_{n}a_{n+1}}$, and the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $T_{n}$. If $\forall n\in\mathbb{N}^{*}$, the inequality $T_{n}-na < 0$ always holds, find the range of the real number $a$.

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