
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 the roots of the equation 
\[ x^{3} - k_{1} x - k_{2} = 0 \quad \text{(where } k_{1} + k_{2} \neq 1 \text{)}. \]
Then find the value of the expression
\[ \frac{1+a}{1-a} + \frac{1+b}{1-b} + \frac{1+c}{1-c} = \]


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