
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 \\(S_n\\) be the sum of the first \\(n\\) terms of the sequence \\(\{a_n\}\\), given that \\(a_n > 0\\) and \\(a_n^2 + a_n = 2S_n\\).

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

\\((2)\\) If \\(b_n = \frac{2}{a_n \cdot a_{n+2}}\\), 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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