
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 that the sequence \\(\{a_n\}\) is an arithmetic sequence, and \\(a_2 + a_5 = 19\), \\(a_3 + a_6 = 25\).

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

\\((2)\\) If the sequence \\(\{a_n - b_n\}\) is a geometric sequence with the first term being \\(2\\) and the common ratio being \\(2\\), find the sum of the first \\(n\\) terms of the sequence \\(\{b_n\}\), denoted as \\(S_n\).

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