
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 $\\{a\_n\\}$ be a geometric sequence with a positive common ratio, where $a\_1=2$ and $a\_3=a\_2+4$.

1. Find the general term formula for $\\{a\_n\\}$.
2. Let $\\{b\_n\\}$ be an arithmetic sequence with the first term $1$ and common difference $2$. 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}
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