
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
Determine the order of the arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM) of three distinct positive numbers \( x \), \( y \), and \( z \), where \( x \neq y \neq z \) and the differences between \( x \), \( y \), and \( z \) are marginal.

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