
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
Let \(x, y\), and \(N\) be real numbers, with \(y\) nonzero, such that the sets \(\left\{(x+y)^{2},(x-y)^{2}, x y, x / y\right\}\) and \(\{4, 12.8, 28.8, N\}\) are equal. Compute the sum of the possible values of \(N\).

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