
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]


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Given a sequence $\{a_{n}\}$ where $a_{1}=1$, $\frac{{a}_{n+1}}{{a}_{n}}=2$, and an arithmetic sequence $\{b_{n}\}$ where $b_{1}=a_{3}$, $b_{2}=a_{1}$. Find:<br/>
$(Ⅰ)$ The general formula for sequences $\{a_{n}\}$ and $\{b_{n}\}$;<br/>
$(Ⅱ)$ The sum of the first $n$ terms of the sequence $\{a_{n}+b_{n}\}$.

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