
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\}\) with the sum of its first \\(n\\) terms denoted as \\(S_n\\), and \\(S_n = n^2 - 14n\\),

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

\\((2)\\) Calculate the sum of the first \\(20\\) terms of the sequence \\(\left\{\dfrac{1}{|a_na_{n+1}|}\right\}\), denoted as \\(T_{20}\\).

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