
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 an arithmetic sequence \\(\{a_n\}\) with the sum of its first \\(n\\) terms denoted as \\(S_n\\), where \\(S_3=15\\), and the arithmetic mean of \\(a_3\\) and \\(a_5\\) is \\(9\\),  
\\((1)\\) find \\(a_n\\) and \\(S_n\\)  
\\((2)\\) Let \\(b_n= \dfrac {4}{a_n^{2}-1} (n\in\mathbb{N}^*)\\), calculate 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}
user