
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 \( f(x) \) be a cubic polynomial, and \( r_1, r_2, r_3 \) be the roots of \( f(x) \). If \(\frac{f\left(\frac{1}{2}\right) + f\left(-\frac{1}{2}\right)}{f(0)} = 1003\), find the value of \(\frac{1}{r_1 r_2} + \frac{1}{r_2 r_3} + \frac{1}{r_3 r_1}\).

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