
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 the complex numbers ${z_1} = 3 - 2i$ and ${z_2} = -2 + 3i$.

(1) Find ${z_1} \cdot {z_2}$;

(2) If a complex number $z$ satisfies $\frac{1}{z} = \frac{1}{{z_1}} + \frac{1}{{z_2}}$, find $|z|$.

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