
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
Let $\{a\_n\}$ be an arithmetic sequence, and $S\_n$ be the sum of the first $n$ terms of the sequence $\{a\_n\}$. Given that $a\_2 + a\_6 = 2$ and $S\_15 = 75$.
(1) Find the general term formula $a\_n$;
(2) If $b\_n = 2a\_n - (2n - 1)$, and $T\_n$ is the sum of the first $n$ terms of the sequence $\{b\_n\}$, find $T\_n$.

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