
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
In the geometric sequence $\{a_n\}$ with common ratio $q > 1$, we have $a_2 = 2$ and the sum of the first three terms $S_3 = 7$.
(1) Find the general term formula for the sequence $\{a_n\}$;
(2) Let $b_n = \log_2 a_n$ and $c_n = \frac{1}{b_{n+1} \cdot b_{n+2}}$, find the sum of the first $n$ terms, denoted as $T_n$, for the sequence $\{c_n\}$.

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