
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
Real numbers  $a$ ,  $b$ ,  $c$  which are differ from  $1$  satisfies the following conditions;
(1)  $abc =1$ (2)  $a^2+b^2+c^2 - \left( \dfrac{1}{a^2} + \dfrac{1}{b^2} + \dfrac{1}{c^2} \right) = 8(a+b+c) - 8 (ab+bc+ca)$ Find all possible values of expression  $\dfrac{1}{a-1} + \dfrac{1}{b-1} + \dfrac{1}{c-1}$ .

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