
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 the sequence $\left\{ a_n \right\}$ is an arithmetic sequence, and $a_1 + a_3 = 8, a_2 + a_4 = 12$.

$(1)$ Find the general formula for $\left\{ a_n \right\}$.

$(2)$ Let $b_n = \frac{a_n}{2^n}$, find the sum of the first $n$ terms of the sequence $\left\{ b_n \right\}$.

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