
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 $\{a\_n\}$ where $a\_1=4$, $a\_n > 0$, and the sum of the first $n$ terms is $S\_n$. If $a\_n= \sqrt {S\_n}+ \sqrt {S\_n-1}(n\geqslant 2)$, find:

1. The general term formula of the sequence $\{a\_n\}$;
2. The sum $T\_n$ of the first $n$ terms of the sequence $\{ \frac {1}{a\_n a_{n+1}}\}$.

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