
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 wooden cube, whose edges are two centimeters long, rests on a horizontal surface. Illuminated by a point source of light that is \(y\) centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of the shadow, which does not include the area beneath the cube, is 200 square centimeters. Find the greatest integer that does not exceed \(1000y\).

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