
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 sequence $\{a\_n\}$ is a geometric sequence, $a\_1=2$, the common ratio $q > 0$, and $a\_2$, $6$, $a\_3$ form an arithmetic sequence.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) Let $b\_n=\log\_2 a\_n$, $T\_n=\frac{1}{b\_1b\_2}+\frac{1}{b\_2b\_3}+\frac{1}{b\_3b\_4}+...+\frac{1}{b\_n b\_{n+1}}$, find the value of $n$ that makes $T\_n < \frac{6}{7}$.

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