
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
The sequence $\{a\_n\}$ is a non-constant arithmetic sequence with $a\_4=10$. Additionally, $a\_3$, $a\_6$, and $a\_10$ form a geometric sequence.
(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) If $b\_n=2^{n}a\_n$, find the sum of the first $n$ terms, denoted as $s\_n$, for the sequence $\{b\_n\}$.

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