
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 positive sequence \( a_{0}, a_{1}, a_{2}, \cdots, a_{n}, \cdots \) that satisfies
\[ 
\sqrt{a_{n} a_{n-2}} - \sqrt{a_{n-1} a_{n-2}} = 2 a_{n-1} \quad (n \geq 2) 
\]
and \( a_{0} = a_{1} = 1 \), find the general term formula for \( \{a_{n}\} \).

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