
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 \(a, b, c\) be arbitrary real numbers such that \(a > b > c\) and \((a - b)(b - c)(c - a) = -16\). Find the minimum value of \(\frac{1}{a - b} + \frac{1}{b - c} - \frac{1}{c - a}\).

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