
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 arithmetic sequence $\left\{a_{n}\right\}$ and the geometric sequence $\left\{b_{n}\right\}$, $a_{1}=b_{1}=1$, $a_{2}=b_{2}$, and $2+a_{4}=b_{3}$.

1. Find the general formulas for $\left\{a_{n}\right\}$ and $\left\{b_{n}\right}$.
2. Find the sum $S_{n}$ of the first $n$ terms of the sequence $\left\{a_{n}+b_{n}\right}$.

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