
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
For how many [ordered pairs](https://artofproblemsolving.com/wiki/index.php/Ordered_pair) $(x,y)$ of [integers](https://artofproblemsolving.com/wiki/index.php/Integer) is it true that $0 < x < y < 10^6$ and that the [arithmetic mean](https://artofproblemsolving.com/wiki/index.php/Arithmetic_mean) of $x$ and $y$ is exactly $2$ more than the [geometric mean](https://artofproblemsolving.com/wiki/index.php/Geometric_mean) of $x$ and $y$?

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