
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
A transformation of the first [quadrant](https://artofproblemsolving.com/wiki/index.php/Quadrant) of the [coordinate plane](https://artofproblemsolving.com/wiki/index.php/Coordinate_plane) maps each point $(x,y)$ to the point $(\sqrt{x},\sqrt{y}).$  The [vertices](https://artofproblemsolving.com/wiki/index.php/Vertex) of [quadrilateral](https://artofproblemsolving.com/wiki/index.php/Quadrilateral) $ABCD$ are $A=(900,300), B=(1800,600), C=(600,1800),$ and $D=(300,900).$  Let $k_{}$ be the area of the region enclosed by the image of quadrilateral $ABCD.$  Find the greatest integer that does not exceed $k_{}.$

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