
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
For which real values of $x$ and $y$, the complex numbers $\quad z_{1}=x^{2}(1-3 i)-10 \quad$ and $\quad z_{2}=y(y-i) \quad$ are opposites?

Illustrate the sets of points for which the following conditions are met ( $10.12-10.16$ ):

$10.12-1 \leq \operatorname{Im} z<2$.

$10.13|z| \leq 2$.

$10.14|z+i|=1.5$.

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