
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\}\) where \\(a_2=5\\) and the sum of the first \\(4\\) terms is \\(S_4=28\\);  
(Ⅰ) Find the general formula for the sequence \\(\{a_n\}\);  
(Ⅱ) Let \\(b_n=2^n\\), and \\(T_n=a_nb_1+a_{n-1}b_2+a_{n-2}b_3+\ldots+a_2b_{n-1}+a_1b_n\\), find \\(T_n\\).

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