
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
Let the sequence of positive numbers \(a_0, a_1, a_2, \cdots\) satisfy \(a_0 = a_1 = 1\) and \(\sqrt{a_n a_{n-2}} - \sqrt{a_{n-1} a_{n-2}} = 2 a_{n-1}\) for \(n = 2, 3, \cdots\). Find the general term formula for this sequence.

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