
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 two distinct positive numbers \(a\) and \(b\), with \(a < b\), let \(A.M.\), \(G.M.\), and \(H.M.\) represent their Arithmetic Mean, Geometric Mean, and Harmonic Mean, respectively. Determine the value of the expression \(\frac{A.M. - G.M.}{A.M. - H.M}\).

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