
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 an arithmetic sequence $\{a\_n\}$ where $a\_1=3$, and the sum of its first $n$ terms is $S\_n$. Also, consider a geometric sequence $\{b\_n\}$ with all positive terms, where $b\_1=1$, $b\_2 + S\_2 = 12$, and $a\_3 = b\_3$.

(I) Find the general terms of the sequences $\{a\_n\}$ and $\{b\_n\}$.
(II) Find the sum $T\_n$ of the first $n$ terms of the sequence $\{ \frac{1}{S\_n} \}$.

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