
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
It is known that there exists a number \( S \), such that if \( a + b + c + d = S \) and \(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = S \) (where \( a, b, c, d \) are different from zero and one), then \(\frac{1}{a - 1} + \frac{1}{b - 1} + \frac{1}{c - 1} + \frac{1}{d - 1} = S \). Find \( S \).

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