
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 with a common ratio of $2$, and $a_2$, $a_3+1$, $a_4$ form an arithmetic sequence.

(1) Find the general term formula for the sequence $\{a_n\}$.
(2) Let $b_n= \frac {1}{\log_{2}a_{n+1} \cdot \log_{2}a_{n+2}}$, calculate the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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