
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 that $z_{1}$ and $z_{2}$ correspond to points $P$ and $Q$ on the complex plane, and $\left|z_{2}\right| = 4$, while $4z_{1}^{2} - 2z_{1}z_{2} + z_{2}^{2} = 0$, find the area of the triangle $\triangle OPQ$ formed by points $P$, $Q$, and the origin $O$.

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