
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 \( a_{1}=a_{2}=\frac{1}{3} \), and for \( n=3,4,5, \cdots \), \( a_{n} = \frac{\left(1-2a_{n-2}\right) a_{n-1}^{2}}{2a_{n-1}^{2}-4a_{n-2}a_{n-1}^{2}+a_{n-2}} \), find the general term formula of the sequence \(\{a_{n}\}\).

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