
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 $Z_1$ and $Z_2$ are two fixed points on the complex plane, and point $Z$ is on the perpendicular bisector of the line segment $Z_1Z_2$. According to the geometric meaning of complex numbers, the relationship between the complex numbers $z$, $z_1$, and $z_2$ corresponding to points $Z$, $Z_1$, and $Z_2$ is:

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