
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
Consider the system of equations where $n$ is a real number:
\[ nx^2 + y = 2 \]
\[ ny^2 + z = 2 \]
\[ nz^2 + x = 2 \]
Determine the value(s) of $n$ for which there is no solution.
**A)** \(0\)  
**B)** \(1\)  
**C)** \(-1\)  
**D)** \(0\) or \(1\)  
**E)** none of these answers

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