
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 two sequences $\left(a_{n}\right)$ and $\left(b_{n}\right)$, one of which is arithmetic and the other geometric.

It is known that $a_{1}=b_{1}$, $\frac{a_{2}}{b_{2}}=2$, and $\frac{a_{4}}{b_{4}}=8$. What can the ratio $\frac{a_{3}}{b_{3}}$ be?

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