
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
A sequence $\{a\_n\}$ is called a "ladder geometric sequence of order $\lambda$" if the equation $a\_{n+λ}^2 = a\_n \times a\_{n+2λ}$ holds for any positive integer $n$ and constant $\lambda (\lambda \in \mathbb{N})$. The value of $\frac{a\_{n+λ}}{a\_n}$ is called the "ladder ratio". If the sequence $\{a\_n\}$ is a 3rd-order ladder geometric sequence with $a\_1 = 1$ and $a\_4 = 2$, find the value of $a\_{10}$.

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