
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
Suppose the sequence $\left\{a_{n}\right\}$, where all terms are positive numbers, satisfies $a_{1}=2$ and $a_{n}=a_{n+1}+a_{n+2}$ for $n \in \mathbf{N}^{*}$. Let $b_{n} = a_{1} a_{2} \cdots a_{n}$, and it is given that $b_{n}^{3} \geqslant 2\sqrt{2}$ holds for $n \geqslant 2$. Find the general term formula of the sequence $\left\{b_{n}\right\}$.

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