
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
For certain real values of  $a, b, c,$  and  $d,$  the equation  $x^4+ax^3+bx^2+cx+d=0$  has four non-real roots.  The product of two of these roots is  $13+i$  and the sum of the other two roots is  $3+4i,$  where  $i=\sqrt{-1}.$   Find  $b.$ 

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