
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 $\{a_{n}\}$ is an arithmetic sequence, $a_{2}=1$, $a_{6}=9$.  
$(Ⅰ)$ Find the general formula for $\{a_{n}\}$.  
$(Ⅱ)$ If the sequence $\{b_{n}\}$ is a geometric sequence with a common ratio of $3$, and $b_{1}=2$. Find the sum of the first $n$ terms of the sequence $\{a_{n}+b_{n}\}$, denoted as $S_{n}$.

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