
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 sequence $\{a\_n\}$ is an arithmetic sequence with a non-zero common difference $d$, and a subsequence formed by some terms of $\{a\_n\}$, denoted as $(a_{b\_1}, a_{b\_2}, ..., a_{b\_n}, ...)$, is a geometric sequence with $b\_1 = 1$, $b\_2 = 5$, $b\_3 = 17$.

1. Find the general term formula for the sequence $\{b\_n\}$.
2. Denote $T\_n = C\_n^1 b\_1 + C\_n^2 b\_2 + C\_n^3 b\_3 + ... + C\_n^n b\_n$, find $T\_n$.

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