
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
The trajectory of complex number $Z$ corresponding to point $Z$ with given complex numbers $Z_1$, $Z_2$ ($Z_1 \neq Z_2$), determined by $|Z-Z_1|=|Z-Z_2|$, find the geometric shape of the locus of $Z$.

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