
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 a geometric sequence $\{a_n\}$, the sum of the first $n$ terms $S_n = \lambda \cdot 2^n - 2$ ($\lambda \neq 0$).  
(1) Find the general term of the sequence $\{a_n\}$.  
(2) Let $b_n = 2\log_2a_n$, $c_n = \frac{1}{b_n^2 - 1}$, 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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