
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
If the sequence $\{a_n\}$ satisfies the equation $a_{n+\lambda}^2=a_{n}\times a_{n+2\lambda}$ for any positive integer $n$ and constant $\lambda$ ($\lambda\in\mathbb{N}$), then the sequence $\{a_n\}$ is called a "λ-step geometric sequence." The value of $\frac{a_{n+\lambda}}{a_{n}}$ is called the "step ratio." If $\{a_n\}$ is a 3-step geometric sequence and $a_{1}=1$, $a_{4}=2$, find the value of $a_{10}$.

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