
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<sub>n</sub>} with a common difference d > 0, and a<sub>2</sub> is the geometric mean of a<sub>1</sub> and a<sub>4</sub>. Let $$b_{n}=a_{2^{n}}$$. If for any n ∈ N*, we have $$\frac {1}{b_{1}}+ \frac {1}{b_{2}}+…+ \frac {1}{b_{n}}<3$$, find the range of d.

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