
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
The sequence $\{a\_n\}$ has a sum of its first $n$ terms denoted as $S\_n$, and $S\_n = 2a\_n - 2$.

1. Find the general formula for the $n$-th term of the sequence $\{a\_n\}$.
2. Let $b\_n = \log\_2 a\_n$ and $c\_n = \frac{b\_n^2}{a\_n}$. 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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