
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]


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A metallic cube, whose edges are two centimeters long, rests on a horizontal surface. It is illuminated by a point source of light that is $x$ centimeters directly above one of its upper vertices. The shadow of the cube, excluding the area beneath the cube itself, on the horizontal surface is 192 square centimeters. Find the greatest integer that does not exceed $1000x$.

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