
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 a sequence ${a_n}$ is $S_n$ and $S_n = 2a_n - 1$ for all $n \in \mathbb{N}^*$.

1. Find the general term formula for the sequence ${a_n}$.
2. If $b_n = \log_2 a_{n+1}$, find the sum of the first $n$ terms, $T_n$, for the sequence $\{\frac{1}{b_n \cdot b_{n+1}}\}$.

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