
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, with each edge two centimeters long, rests on a horizontal surface. It is illuminated by a point source of light placed $x$ centimeters directly above a vertex on the top of the cube. The resulting shadow on the horizontal surface, excluding the area right beneath the cube, is 200 square centimeters. Determine $\lfloor 1000x \rfloor$, the greatest integer not exceeding $1000x$.

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