
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 formula for the sequence $\{a_n\}$.  
(2) Let $b_n=\log_{2}a_n$, and $$T_{n}= \frac {1}{b_{1}b_{2}}+ \frac {1}{b_{2}b_{3}}+ \frac {1}{b_{3}b_{4}}+\ldots+ \frac {1}{b_{n}b_{n+1}}$$, find the value of $n$ for which $$T_{n}< \frac {6}{7}$$.

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