
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
Let the sequence \\( \{a_n\} \\) satisfy the condition \\( a_1=1 \\), \\( a_{n+1}=a_n+3\cdot2^{n-1} \\).
\\((1)\\) Find the general formula for the sequence \\( \{a_n\} \\).
\\((2)\\) If \\( \frac{b_n}{a_n}=n \\), find the sum of the first \\( n \\) terms of the sequence \\( \{b_n\} \\), \\( S_n \\).

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