
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 an arithmetic sequence $\{a\_n\}$ with a common difference of $d=2$, its sum of the first $n$ terms is $S\_n$. Meanwhile, a geometric sequence $\{b\_n\}$ satisfies $b\_1=a\_1$, $b\_2=a\_4$, and $b\_3=a\_13$.

(I) Find the general term formula for the sequence $\{a\_n\}$ and the sum of the first $n$ terms, $B\_n$, for the sequence $\{b\_n\}$.

(II) Denote the sum of the first $n$ terms of the sequence $\{ \frac{1}{S\_n} \}$ as $T\_n$. Find $T\_n$.

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