
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 a positive sequence \\(\{a_n\}\) whose sum of the first \\(n\\) terms is \\(S_n\\), and \\(\sqrt{S_n}\\) is the arithmetic mean of \\(1\\) and \\(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 \\(\left\{ \frac{2}{a_na_{n+1}} \right\}\).

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