
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 a number \(N\), not equal to zero, such that the difference between the square of \(N\) and twice its reciprocal equals a given real constant \(R\). Find the sum of all possible values of \(N\) for this \(R\).

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