
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]


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The sequence $\{a\_n\}$ is an arithmetic sequence with first term $1$ and common difference $d$. The first three terms of the geometric sequence $\{b\_n\}$ are $a\_1$, $a\_2-1$, and $a\_3-1$.

1. Find the general term formula for $\{a\_n\}$;
2. Find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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