
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
Find all ordered triples $(a, b, c)$ of non-zero real numbers such that $a = \sqrt{bc}$, $b = \sqrt{ca}$, and $c = \sqrt{ab}$, with the constraint that exactly one of $a, b, c$ must be negative.
**A)** 0  
**B)** 1  
**C)** 2  
**D)** 3

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