
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 complex numbers $\mathrm{z}_{1}$ and $\mathrm{z}_{2}$ that satisfy the following conditions: $\left|\mathrm{z}_{1}\right|=2$, $\left|\mathrm{z}_{2}\right|=3$, and $3 \mathrm{z}_{1}-2 \mathrm{z}_{2}=2-\mathrm{i}$, find the value of $\mathrm{z}_{1} \mathrm{z}_{2}$.

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