
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 three positive real numbers whose sum is 1. If no one of these numbers is more than three times any other, find the maximum value of the product \(xyz\).

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