
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 that \( a, b, c, d \) are certain real values, the equation \( x^{4}+a x^{3}+b x^{2}+c x+d=0 \) has 4 non-real roots. Among these roots, the product of 2 of the roots is \( 13 + \mathrm{i} \) and the sum of the other 2 roots is \( 3 + 4\mathrm{i} \). Here, \( \mathrm{i} \) represents the imaginary unit. Find \( b \).

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