
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 the first term of a geometric sequence $\{a\_n\}$ is $\frac{1}{2}$ and it is a decreasing sequence. Also, $a\_1, \frac{3}{2}a\_2, 2a\_3$ form an arithmetic sequence. The sum of the first $n$ terms of the sequence $\{b\_n\}$ is $S\_n$, where $S\_n=n^2+n$, $n\in\mathbb{N}^*$.
(I) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$.
(II) If $c\_n=\frac{b_{n+1}}{2}\cdot\log_{2}a\_n$, find the sum of the first $n$ terms, $T\_n$, of the sequence $\{\frac{1}{c\_n}\}$.

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