
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. A point source of light is positioned $y$ centimeters directly above the center of the top face of the cube. The area of the shadow cast on the horizontal surface, not including the area under the cube, is 147 square centimeters. Find the greatest integer that does not exceed $1000y$.

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