
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
If a number \(N, N \ne 0\), multiplied by three and increased by five times its reciprocal, equals a given real constant \(S\), then find the sum of all such possible values of \(N\).
A) \( \frac{S}{5} \)
B) \( \frac{S}{3} \)
C) \( 5S \)
D) \( 3S \)

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