
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 sequence \\(\{a_n\}\) where each term is positive and the sum of the first \\(n\\) terms is \\(S_n\), it is known that \\(S_n = a_n^2 + \frac{1}{2}a_n\), where \\(n \in \mathbb{N}^*\).

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

\\((2)\\) Let the sequence \\(\{b_n\}\) be defined as \\(b_n = \frac{1}{a_n \cdot a_{n+1}}\), 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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