
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 a sequence \\(\{a_n\}\\) with the sum of the first \\(n\\) terms being \\(S_n\\), and it satisfies \\(a_1=1\\) and \\(a_n \cdot a_{n+1} = 2S_n\\). Let \\(b_n = \dfrac{2a_n-1}{3^{a_n}}\\), then the sum of the first \\(n\\) terms of the sequence \\(\{b_n\}\\) is \_\_\_\_\_.

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