
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. It's illuminated by a point source of light that is $y$ centimeters directly above an upper vertex of the cube. The cube casts a shadow on the horizontal surface, and the area of the shadow, excluding the area beneath the cube, is 112 square centimeters. Find the greatest integer that does not exceed $1000y$.

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