
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 $i$ is the imaginary unit, complex numbers $z_1=2i$, $z_2=1-3i$, $z_3=1-2i$, and $$\frac {x}{z_{1}} - \frac {5}{z_{2}} = \frac {y}{z_{3}}$$  
(1) Find the real numbers $x$, $y$;  
(2) Calculate $\overline{z_{1}} \cdot \overline{z_{2}}$.

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