
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 an arithmetic sequence $\{a_{n}\}$ with a non-zero common difference, if $a_{1}=1$, and $a_{1}$, $a_{2}$, $a_{5}$ form a geometric sequence.
1. Find the general term formula for the sequence $\{a_{n}\}$.
2. Let $b_{n}=2^{n}$, find the sum of the first $n$ terms $S_{n}$ for the sequence $\{a_{n}+b_{n}\}$.

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