
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 \(a, b,\) and \(c\) be the roots of the polynomial \(x^3 - 6x^2 + 11x - 6 = 0\). Find the value of
\[
\frac{a}{bc + 2} + \frac{b}{ac + 2} + \frac{c}{ab + 2}.
\]

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