
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 a geometric series with positive terms $\{b_n\}$ whose sum of the first $n$ terms is $S_n$. Given $b_3 = 4$ and $S_3 = 7$, let another sequence $\{a_n\}$ satisfy $a_{n+1} - a_n = n + 1$  $(n \in \mathbb{N}^*)$, and $a_1 = b_1$.  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$.  
(Ⅱ) Find the sum of the first $n$ terms of the sequence $\left\{\frac{1}{a_n}\right\}$.

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