
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 $\{a_{n}\}$, where $a_{10}=19$, the common difference $d \neq 0$, and $a_{1}$, $a_{2}$, $a_{5}$ form a geometric sequence.

(1) Find $a_{n}$;

(2) Let $b_{n}=a_{n}2^{n}$, find the sum of the first $n$ terms of the sequence $\{b_{n}\}$, denoted as $S_{n}$.

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