
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 the sequences $\{a\_n\}$ and $\{b\_n\}$ that satisfy $a\_1a\_2a\_3…a\_n=2^{b\_n}$ (n∈N*), if the sequence $\{a\_n\}$ is a geometric sequence, with $a\_1=2$, $b\_3=b\_2+3$.
(I) Find the general terms of the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) Let $c\_n=a\_n+\frac{1}{b\_n}$ (n∈N*), find the sum of the first n terms $T\_n$ of the sequence $\{c\_n\}$.

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