
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
Solve the complex equation \( z(z+i)(z+4i) = 1500i \). If one of the zeros is of the form \( a+bi \) where \( a \) and \( b \) are positive real numbers, find \( a \).
A) \( \sqrt{100} \)
B) \( \sqrt{500} \)
C) \( \sqrt{1500} \)
D) \( \sqrt{2000} \)

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