
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
Let \( z \) be a complex number satisfying \( 15|z|^2 = 3|z+3|^2 + |z^2+4|^2 + 25 \). What is the value of \( z + \frac{8}{z} \)?
A) -8
B) -4
C) 0
D) 4
E) 8

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