
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
A sequence of positive numbers \( a_{0}, a_{1}, a_{2}, \cdots, a_{n}, \cdots \) satisfies the following condition:
$$
\sqrt{a_{n} a_{n-2}}-\sqrt{a_{n-1} a_{n-2}}=2 a_{n-1} \quad(n \geq 2) .
$$

Additionally, \( a_{0} = a_{1} = 1 \). Find the general term of the sequence \( \{a_{n}\} \).

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