
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 sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n$, and $S_n = 2a_n - 2$ ($n \in \mathbb{N}^*$),

1. Find the general term formula for $\{a_n\}$;
2. Let $b_n = \log_2 a_n$, $c_n = \frac{1}{(2b_n - 1)(2b_n + 1)}$, and $T_n$ is the sum of the first $n$ terms of the sequence $\{c_n\}$. If $T_n < \lambda$ holds true for any $n \in \mathbb{N}^*$, find the minimum value of $\lambda$.

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