
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 the sequence \\(\{a_n\}\) have a sum of the first \\(n\\) terms \\(S_n = 2^{n+1} - 2\\), and the sequence \\(\{b_n\}\) satisfies \\(b_n = \frac{1}{(n+1)\log_2{a_n}}\).

\\((1)\\) Find the general formula for the sequence \\(\{a_n\}\).

\\((2)\\) Find the sum of the first \\(n\\) terms \\(T_n\\) of the sequence \\(\{b_n\}\).

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