
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 geometric sequence with the first term $a\_1=4$, and $S\_3$, $S\_2$, $S\_4$ form an arithmetic sequence.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) Let $b\_n=\log \_{2}|a\_{n}|$, and $T\_n$ is the sum of the first $n$ terms of the sequence $\{\frac{1}{b\_n\cdot b\_{n+1}}\}$, find $T\_n$.

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