
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 three prime numbers \(a\), \(b\), and \(c\) such that \(a + b + c + abc = 99\), find the value of \(\left|\frac{1}{a} - \frac{1}{b}\right| + \left|\frac{1}{b} - \frac{1}{c}\right| + \left|\frac{1}{c} - \frac{1}{a}\right|\).

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