
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 given by:
\[ nx + y + z = 1, \]
\[ x + ny + z = 1, \]
\[ x + y + nz = 1. \]
Find the values of \( n \) for which this system of equations has no solution.
**A)** \( -2 \)
**B)** \( 1 \)
**C)** \( 0 \)
**D)** All real numbers
**E)** None of these

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