
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
(1) $i$ is the imaginary unit. Given the complex number $z = \frac{15 - 5i}{(2 + i)^2}$, and $ω = z^2 + 3\overline{z} - 1$, find the coordinates of the point corresponding to $ω$ in the complex plane.
(2) $i$ is the imaginary unit. Given the complex number $z$ that satisfies the equation $z \cdot \overline{z} - 2zi = 1 + 2i$, find the complex number $z$.

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