
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 numbers, the equation \( x^4 + ax^3 + bx^2 + cx + d = 0 \) has four non-real roots. Among these roots, the product of two of them is \( 13 + i \) and the sum of the other two is \( 3 + 4i \), where \( i \) is the imaginary unit. Find \( b \).

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