
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 that integers $a, b, c$ satisfy the inequality $1 < a < b < c$ and the product $(ab-1)(bc-1)(ca-1)$ is divisible by $abc$, find the values of $a, b, c$.

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