
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 that $\{a\_n\}$ is an arithmetic sequence with a common difference greater than $0$ and satisfies $a\_3a\_6=55$, $a\_2+a\_7=16$.
(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) If sequence $\{a\_n\}$ and sequence $\{b\_n\}$ satisfy the equation: $a\_n= \frac {b\_1}{2}+ \frac {b\_2}{2^{2}}+ \frac {b\_3}{2^{3}}+… \frac {b\_n}{2^{n}}(n$ is a positive integer$)$, find the sum of the first $n$ terms, $S\_n$, of sequence $\{b\_n\}$.

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