
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
Consider the sequence of positive terms $\{a\_n\}$ that satisfies the equation: $a\_n^2 - (2n - 1)a\_n - 2n = 0$.
(1) Find the general term formula, $a\_n$, for the sequence $\{a\_n\}$.
(2) Define a new sequence $\{b\_n\}$, where $b\_n = 2^{n-1}a\_n - n$. Find the sum of the first $n$ terms, $T\_n$, for this new sequence.

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