
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
Consider a wooden cube, whose edges are two centimeters long, resting on a horizontal surface. A point source of light is positioned `x` centimeters directly above an upper vertex of the cube. This set-up results in the cube casting a shadow on the horizontal surface, the area of which, excluding the area beneath the cube, is 200 square centimeters. Determine the greatest integer that does not exceed `100x`.

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