
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
Let $z_1$ and $z_2$ be two complex numbers, given that $z_1 = 3-4i$, $|z_2| = 5$, and the product $z_{1} \cdot \overline{z_{2}}$ is a pure imaginary number.
(Ⅰ) Find $z_2$;
(Ⅱ) Let the complex number $z = x + yi$ (where $x, y \in \mathbb{R}$) correspond to the moving point $Z(x, y)$ on the complex plane. Determine the trajectory of the moving point $Z$ that satisfies $|z - z_2| = 3$ and its trajectory equation.

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