
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
For the positive sequence \\(\{a_n\}\) that satisfies \\(a_n^2-(2n-1)a_n-2n=0\),

\\((1)\\) Find the general formula for \\(a_n\\);

\\((2)\\) Let \\(b_n = \frac{1}{(n+1)a_n}\\), 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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