
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 \(\left\{a_{n}\right\}\) with a common difference \(d\) being a positive integer, and a geometric sequence \(\left\{b_{n}\right\}\), where \(a_{1} = b_{1}\) and \(a_{2} = b_{2}\). If \(d\) can be 2, 3, 4, or 5, determine the value(s) of \(d\) such that every term in \(\left\{b_{n}\right\}\) is also a term in \(\left\{a_{n}\right\}\).

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