
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 \(z_1 = -3 + 4i\) and \(z_2 = 2 - i\), find an equation in the form \(az + b\overline{z} = c\) where \(a\), \(b\), and \(c\) are some complex numbers that represents the line joining \(z_1\) and \(z_2\), and determine the product \(ab\).

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