
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]


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Given that the sequence $\{a\_n\}$ is a positive geometric sequence, it satisfies $a\_3=4$, and $a\_5$, $3a\_4$, $a\_6$ form an arithmetic sequence. The sequence $\{b\_n\}$ satisfies $b\_n=\log\_2{a\_n}+\log\_2{a\_{n+1}}$.

(I) Find the general terms of the sequences $\{a\_n\}$ and $\{b\_n\}$;

(II) If the sum of the first $n$ terms of the sequence $\{b\_n\}$ is $S\_n$, and the sequence $\{c\_n\}$ satisfies $c_{n}= \frac {1}{4S_{n}-1}$, find the sum of the first $n$ terms of the sequence $\{c\_n\}$, denoted as $T\_n$.

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