
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
\[S=\frac{1}{5-\sqrt{23}}+\frac{1}{\sqrt{23}-\sqrt{20}}-\frac{1}{\sqrt{20}-4}-\frac{1}{4-\sqrt{15}}+\frac{1}{\sqrt{15}-\sqrt{12}}-\frac{1}{\sqrt{12}-3}.\]
Determine $S$ among the choices.
A) $S = 1$
B) $S = 2\sqrt{23} - 2$
C) $S = \frac{1}{60}$
D) $S < 0$
E) $S > 10$

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