
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
What quadratic polynomial whose coeﬃcient of  $x^2$  is  $1$  has roots which are the complex conjugates of the solutions of  $x^2 -6x+ 11 = 2xi-10i$ ? (Note that the complex conjugate of  $a+bi$  is  $a-bi$ , where a and b are real numbers.)

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