
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 sum of the first $n$ terms of a positive geometric sequence $\{b_{n}\}$ is $S_{n}$, with $b_{3} = 4$ and $S_{3} = 7$. Another sequence $\{a_{n}\}$ satisfies $a_{n+1} - a_{n} = n + 1$ for all natural numbers $n$, and $a_{1} = b_{1}$.

(I) Find the general term formula for the sequence $\{a_{n}\}$.

(II) Find the sum of the first $n$ terms of the sequence $\{\frac{1}{a_{n}}\}$.

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