
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
Determine the real numbers \( b \) for which all complex roots of the equation
\[ z^4 - 10z^3 + 16bz^2 - 2(3b^2 - 5b + 4)z + 6 = 0 \]
form the vertices of a rectangle (or square) in the complex plane.

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