
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
How many ordered quadruples $(a, b, c, d)$ of non-zero real numbers are there such that $a^2b=c$, $bc^2=a$, $ca^2=b$, and $a + b + c = d$?
A) $(1, 1, 1, 3)$  
B) $(-1, -1, -1, -3)$  
C) $(1, -1, 1, 1)$  
D) $(i, i, i, 3i)$  (Where $i$ is the imaginary unit)

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