
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 real numbers \( a \), \( b \), and \( c \) that satisfy
\[ 
abc \neq 0, \quad a + b + c = a^2 + b^2 + c^2 = 2, 
\]
determine the value of 
\[ 
\frac{(1-a)^2}{bc} + \frac{(1-b)^2}{ca} + \frac{(1-c)^2}{ab}.
\]

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