
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
The distinct positive integers  $a$  and  $b$  have the property that   $$ \frac{a+b}{2},\quad\sqrt{ab},\quad\frac{2}{\frac{1}{a}+\frac{1}{b}} $$   are all positive integers. Find the smallest possible value of  $\left|a-b\right|$ .

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