
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, where the sum of the first $n$ terms is represented by $S\_n$, and $a\_n = 2\sqrt{2S\_n} - 2$.

1. Write out the first three terms of the sequence $\\{ a\_n \\}$.
2. Find the general formula for the sequence $\\{ a\_n \\}$.
3. If $\\{ b\_n \\}$ is a sequence where $b\_n = \frac{4}{a\_n a\_{n+1}}$, find the sum of the first $n$ terms of $\\{ b\_n \\}$, denoted as $T\_n$.

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