
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
Determine the set of values of $n$ for which the polynomial $x^2 + 2xy + nx^2 + y^2 + 2y - n^2$ can be factored into two factors, both linear in $x$ and $y$, and with integer coefficients.
A) $0, 2$ \
B) $0, \pm 2$ \
C) $2, -2$ \
D) None of these

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