
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 the sequence $\left\{a_{n}\right\}$ satisfying $a_{1}=1$, $a_{2}=\frac{1+\sqrt{5}}{2}$, and $(\sqrt{5}-1) a_{n}^{2} a_{n-2}=2 a_{n-1}^{3}$, find the general term formula for the sequence $\left\{a_{n}\right\}$, $a_{n}=$ .

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