
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 $\{a\_n\}$, it is known that $a_{n+1} > a_{n}$, $a_{1} \cdot a_{10} = 160$, and $a_{3} + a_{8} = 37$.

(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) If a new sequence $\{b\_n\}$ is formed by taking the 2nd, 4th, 8th, and $2^n$th terms from the original sequence $\{a\_n\}$ in their original order, find the sum $S\_n = b\_1 + b\_2 + \dots + b\_n$.

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