
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 \\(\{a_n\}\) is a geometric sequence composed of positive numbers, \\(a_2=2\\), and \\(a_4, 3a_3, a_5\\) form an arithmetic sequence.

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

(2) The sum of the first \\(n\\) terms of the sequence \\(\{a_{n+1}-\lambda a_n\}\) is \\(S_n\\). If \\(S_n=2^n-1 (n\in \mathbb{N}^*)\\), find the value of the real number \\(\lambda\).

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