
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 \( x, y, z \) be real numbers such that
\[ x + y + z = 1 \quad \text{and} \quad x^2 + y^2 + z^2 = 1. \]
Let \( m \) denote the minimum value of \( x^3 + y^3 + z^3 \). Find \( 9m \).

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