
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
Consider a cubic polynomial \( x^3 - sx^2 + px - q \) whose roots \( r_1, r_2, \) and \( r_3 \) satisfy \( r_1 + r_2 + r_3 = r_1^2 + r_2^2 + r_3^2 \). Calculate the maximum possible value of \( \frac{1}{r_1^3} + \frac{1}{r_2^3} + \frac{1}{r_3^3} \).

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