
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 $\{a\_n\}$, denoted as $S\_n$, satisfies the equation $S\_n = 2a\_n - 1$, where $n \in \mathbb{N}^*$.

(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Let $b\_n = \log\_2 a\_n$, where $n \in \mathbb{N}^*$, find the sum of the first $2n$ terms of the sequence $\{(-1)^n b\_n^2\}$, denoted as $T\_2n$.

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