
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 a non-zero common difference arithmetic sequence {a<sub>n</sub>}, where a<sub>1</sub> = 1, and a<sub>1</sub>, a<sub>3</sub>, a<sub>9</sub> form a geometric sequence.
(1) Find the general term formula for the sequence {a<sub>n</sub>};
(2) Let b<sub>n</sub> = $2^{a_{n}}$ + n, find the sum of the first n terms S<sub>n</sub> for the sequence {b<sub>n</sub>}.

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