
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
Let $\left\{a_{n}\right\}$ be a geometric sequence with a positive common ratio, where $a_{1}=2$ and $a_{3}=a_{2}+4$.
1. Find the general formula for $\left\{a_{n}\right\}$.
2. Let $\left\{b_{n}\right\}$ be an arithmetic sequence with the first term $1$ and common difference $2$. Determine the sum of the first $n$ terms of the sequence $\left\{a_{n}+b_{n}\right\}$ denoted by $S_{n}$.

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