
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 common difference $d \neq 0$, $a_{1}=2$, and $a_{1}$, $a_{3}$, $a_{9}$ form a geometric sequence.
(1) Find the general term formula for the sequence $\{a_{n}\}$;
(2) Sequence $\{b_{n}\}$ satisfies $b_{n}=2^{a_{n}}+1$, find the sum of the first $n$ terms $s_{n}$.

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