
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 the complex numbers \(z_{1}, z_{2}\) corresponding to points \(A, B\) on the complex plane, and \(\left|z_{1}\right|=2\), \(z_{1}^{2}-2z_{1}z_{2}+4z_{2}^{2}=0\), with \(O\) as the origin, find the perimeter of \(\triangle OAB\).

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