
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
It is known that the sequence \\(\{a_n\}\) is an arithmetic sequence with \\(a_3=5\) and \\(a_7=13\). The sequence \\(\{b_n\}\)'s sum of the first \\(n\) terms is \\(S_n\), and it satisfies \\(S_n=2b_n-1\).
\\(1)\\) Find the general term formulas for \\(\{a_n\}\) and \\(\{b_n\}\).
\\(2)\\) If \\(c_n=a_nb_n\), and the sum of the first \\(n\) terms of \\(\{c_n\}\) is \\(T_n\), find the expression for \\(T_n\).

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