
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 a sequence of positive numbers $a_{0}, a_{1}, a_{2}, \cdots$ where $a_{0}=a_{1}=1$ and
$$
\sqrt{a_{n} a_{n-2}}-\sqrt{a_{n-1} a_{n-2}}=2 a_{n-1}, \quad n=2,3, \cdots,
$$
find the general term of this sequence.

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