
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 geometric sequence \\(\{a_n\}\) with a first term of \\(1\\), and a sequence \\(\{b_n\}\) that meets the conditions \\(b_1=2\\), \\(b_2=5\\), and \\(a_n(b_{n+1}-b_n)=a_{n+1}\\), find the sum of the first \\(n\\) terms of the sequence \\(\{b_n\}\).

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