
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
There are three unknowns \( x, y, z \) that satisfy the following equations:
$$
\left\{\begin{array}{l}
x + y + z = a, \\
x^{2} + y^{2} + z^{2} = b^{2}, \\
x^{-1} + y^{-1} + z^{-1} = c^{-1}.
\end{array}\right.
$$

Determine the value of \( x^{3} + y^{3} + z^{3} \).

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