
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
Complete the following syllogism:
Major Premise: The product of two conjugate complex numbers is a real number.
Minor Premise: $x+yi$ and $x-yi$ are conjugate complex numbers.
Conclusion: _____

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