
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 arithmetic sequence $\{a_n\}$ satisfies $a_2=0$ and $a_6 + a_8 = 10$.
(1) Find the general formula for the $\{a_n\}$ sequence;
(2) Find the sum of the first $n$ terms for the sequence $\left\{\frac{a_n}{2^{n-1}}\right\}$.

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