
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 complex numbers $z_1$ and $z_2$ correspond to points A and B on the complex plane, respectively, and $|z_1|=4$, $4z_1^2-2z_1z_2+z_2^2=0$. Find the area of $\triangle OAB$.

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