
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 the real numbers \( a, b, c \) satisfy \( a + b + c = 6 \), \( ab + bc + ca = 5 \), and \( abc = 1 \), determine the value of \( \frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} \).

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