
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
In the sequence \\(\{a_n\}\\), where \\(a_1=1\\) and \\(a_n+a_{n+1}=(\frac{1}{5})^n(n\in\mathbb{N}^*)\\), let \\(S_n=a_1+5a_2+5^2a_3+\ldots+5^{n-1}a_n\\). Find the value of \\(\frac{6S_n-5^n a_n}{n}=\\) ______.

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