
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 $d$ satisfying $d>0$, and $a_{2}$ is the geometric mean of $a_{1}$ and $a_{4}$. Let $b_{n}=a_{2^{*}}\left(n \in \mathbf{Z}_{+}\right)$, for any positive integer $n$, it holds that $\frac{1}{b_{1}}+\frac{1}{b_{2}}+\cdots+\frac{1}{b_{n}}<2$. Determine the range of the common difference $d$.

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