
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
Given a non-zero number $N$ such that six times the number plus twice its reciprocal equals a real number $S$, find the sum of all possible values of $N$ for a specified $S$.
A) $\frac{S}{3}$
B) $2S$
C) $\frac{S}{6}$
D) $\frac{6}{S}$

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