
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
Let $\{a_n\}$ be a sequence composed of positive numbers, with the sum of the first $n$ terms denoted as $S_n$ and $$a_{n}=2 \sqrt {2S_{n}}-2$$;  
(Ⅰ) Write down the first three terms of the sequence $\{a_n\}$;  
(Ⅱ) Find the general formula for the sequence $\{a_n\}$ and show the derivation process;  
(Ⅲ) Let $$b_{n}= \frac {4}{a_{n}\cdot a_{n+1}}$$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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